Let’s start with creating an empty MVC Project.Open your visual studion and add a simple Mvc project.
I have also created a folder for storing the uplaoded pdf files on server.

View Html Code

@model  IEnumerable<WebAppMvc.Controllers.FilesInoformation>

@{
    ViewBag.Title = "";
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js"></script>
@using (Html.BeginForm("UploadPdf", "Home", FormMethod.Post,
                                                    new { enctype = "multipart/form-data" }))
{
    @Html.AntiForgeryToken()
    <fieldset>
        <legend>Upload a Pdf file By Ajax</legend>
        <div class="editor-field">
            @Html.TextBox("pdffile", "", new { type = "file", accept = "application/pdf" })
        </div>
        <br />
        <br />
        <div class="editor-field">
            <input type="button" id="btnfileUpload" value="Upload Pdf" />
        </div>
        <div class="row">
            <h3>Uploaded Filles</h3>
            <table class="table">
                <thead>
                    <tr>
                        <th>FileName</th>
                        <th>Action</th>
                    </tr>
                </thead>
                @if (Model != null)
                {
                    foreach (var file in Model)
                    {
                        <tr>
                            <td>@file.filename</td>
                            <td><a href="@file.filepath">View Pdf</a></td>
                        </tr>
                    }
                }
            </table>
        </div>
    </fieldset>
    <script>

        $(document).ready(function(){
            $('#btnfileUpload').click(function () {
                if (window.FormData !== undefined) {
                    var fileUpload = $("#pdffile").get(0);
                    var files = fileUpload.files;
                    var fileData = new FormData();
                    for (var i = 0; i < files.length; i++) {
                        fileData.append(files[i].name, files[i]);
                    }
                    $.ajax({
                        url: '/Home/UploadPdfFiles',
                        type: "POST",
                        contentType: false, 
                        processData: false, 
                        data: fileData,
                        success: function (result) {
                            alert(result);
                            window.location.reload();
                        },
                        error: function (err) {
                            alert(err.statusText);
                        }
                    });
                } else {
                    alert("Your browser doesn support FormData");
                }
            });
        });
    </script>
}

Controller Code

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Web;
using System.Web.Mvc;

namespace WebAppMvc.Controllers
{

    public class FilesInoformation
    {
        public string filename { get; set; }
        public string filepath { get; set; }
    }
    public class HomeController : Controller
    {
        // GET: Home
        public ActionResult Index()
        {
            //getting the list of file uploaded 
            DirectoryInfo directory = new DirectoryInfo(Server.MapPath(@"~\PdfFiles"));
            var files = directory.GetFiles().ToList();
            List<FilesInoformation> model = new List<FilesInoformation>();
            foreach (var file in files)
            {
                model.Add(new FilesInoformation { filename = file.Name, filepath = "/PdfFiles/" + file.Name });
            }
            return View(model);
        }

        [HttpPost]
        public ActionResult UploadPdfFiles()
        {
            // Checking if  Request object  has file
            if (Request.Files.Count > 0)
            {
                try
                {
                    HttpFileCollectionBase files = Request.Files;
                    //in case if you want upload the multiple pdf files
                    for (int i = 0; i < files.Count; i++)
                    {
                        HttpPostedFileBase file = files[i];
                        string fname = file.FileName;
                        // Get the complete folder path and store the file inside it.  
                        fname = Path.Combine(Server.MapPath("~/PdfFiles/"), fname);
                        file.SaveAs(fname);
                    }
                    return Json("Pdf Uplaoded Successfully!");
                }
                catch (Exception ex)
                {
                    return Json(ex.Message);
                }
            }
            else
            {
                return Json("No files selected.");
            }
        }

    }
}

Download Source Code 

Result