Hi Jilsoft,

Using the article i have created the example.

Call (Consume) Web API in ASPX Page in ASP.Net Web Forms using C#

Model

Public Class CustomerModel
    Private newPropertyValue As String
    Public Property Name As String
End Class

Web API Controller

Imports System.Net
Imports System.Web.Http

Public Class CustomerAPIController
    Inherits ApiController
    <Route("api/CustomerAPI/GetCustomers")>
    <HttpPost>
    Public Function GetCustomers(ByVal customer As CustomerModel) As List(Of Customer)
        Dim entities As NorthwindEntities = New NorthwindEntities()
        Return (From c In entities.Customers.Take(10)
                Where c.ContactName.StartsWith(customer.Name) OrElse String.IsNullOrEmpty(customer.Name)
                Select c).ToList()
    End Function
End Class

Global.asax

Imports System.Web.Http
Imports System.Web.Optimization

Public Class WebApiApplication
    Inherits System.Web.HttpApplication
    Sub Application_Start()
        AreaRegistration.RegisterAllAreas()
        GlobalConfiguration.Configure(AddressOf WebApiConfig.Register)
        RouteConfig.RegisterRoutes(RouteTable.Routes)
    End Sub
End Class

HTML

Name:
<asp:TextBox ID="txtName" runat="server"></asp:TextBox>
<asp:Button ID="btnSearch" runat="server" Text="Search" OnClick="Search" />
<hr />
<asp:GridView ID="gvCustomers" runat="server" AutoGenerateColumns="false">
    <Columns>
        <asp:BoundField DataField="CustomerID" HeaderText="CustomerID" />
        <asp:BoundField DataField="ContactName" HeaderText="Contact Name" />
        <asp:BoundField DataField="City" HeaderText="City" />
    </Columns>
</asp:GridView>

Namespaces

Imports System.Net
Imports System.Text
Imports System.Web.Script.Serialization

Code

Protected Sub Page_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        Me.PopulateGridView()
    End If
End Sub

Protected Sub Search(ByVal sender As Object, ByVal e As EventArgs)
    Me.PopulateGridView()
End Sub

Private Sub PopulateGridView()
    Dim apiUrl As String = "http://localhost:52730/api/CustomerAPI"
    Dim input As Object = New With {Key _
        .Name = txtName.Text.Trim()
    }
    Dim inputJson As String = (New JavaScriptSerializer()).Serialize(input)
    Dim client As WebClient = New WebClient()
    client.Headers("Content-type") = "application/json"
    client.Encoding = Encoding.UTF8
    Dim json As String = client.UploadString(apiUrl & "/GetCustomers", inputJson)
    gvCustomers.DataSource = (New JavaScriptSerializer()).Deserialize(Of List(Of Customer))(json)
    gvCustomers.DataBind()
End Sub

Public Class Customer
    Public Property CustomerID As String
    Public Property ContactName As String
    Public Property City As String
End Class

Screenshot