Hi,

Please refer below code.

I have referred below article

Populate (Bind) ASP.Net ListBox using jQuery AJAX and JSON in C# and VB.Net

HTML

<div>
    <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js" type="text/javascript"></script>
    <script type="text/javascript">
        function ShowData() {
            $.ajax({
                type: "POST",
                url: "Default.aspx/GetData",
                data: '{}',
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                success: OnSuccess,
                failure: function (response) {
                    alert(response.d);
                }
            });
        }
        function OnSuccess(response) {
            var data = response.d;
            $('[id*=LB_AvailFields]').empty();
            var listBox = $('[id*=LB_AvailFields]');
            $.map(data, function (item) {
                var option = document.createElement('option');
                option.text = item.PMSystemName;
                listBox[0].add(option);
            });
        }
    </script>
    <asp:ListBox ID="LB_AvailFields" runat="server"></asp:ListBox>
    <input id="btnGetData" type="button" value="Show Data" onclick="ShowData()" />
</div>

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        List<MyListItem> LB = new List<MyListItem>();
        MyListItem lbitem;
        for (int i = 0; i < 5; i++)
        {
            lbitem = new MyListItem();
            lbitem.PMKey = "Key" + i;
            lbitem.PMSystemName = "SystemName: " + i;
            LB.Add(lbitem);
        }
        LB_AvailFields.DataSource = LB;
        LB_AvailFields.DataTextField = "PMSystemName";
        LB_AvailFields.DataValueField = "";
        LB_AvailFields.DataBind();
        HttpContext.Current.Session["LB_AvailFields"] = LB_AvailFields;
    }
}

[System.Web.Services.WebMethod(EnableSession = true)]
public static List<MyListItem> GetData()
{
    List<MyListItem> LB = new List<MyListItem>();
    MyListItem lbitem;
    for (int i = 0; i < 8; i++)
    {
        lbitem = new MyListItem();
        lbitem.PMKey = "Key" + i;
        lbitem.PMSystemName = "SystemName: " + i;
        LB.Add(lbitem);
    }
    return LB;
}

public class MyListItem
{
    public string PMKey { get; set; }
    public string PMSystemName { get; set; }
}

Screenshot