iTextSharp Error: There was an error opening this document. The file is damaged and could not be repaired

You need to Bind the GridView and Render GridView Control before StringReader, also need to close the Document.

Refer the updated code.

protected void ExportToPDF(object sender, EventArgs e)
{
    using (StringWriter sw = new StringWriter())
    {
        using (HtmlTextWriter hw = new HtmlTextWriter(sw))
        {
            Grid_Live.AllowPaging = false;
            this.ReadData();
            Grid_Live.RenderControl(hw);
            StringReader sr = new StringReader(sw.ToString());
            Document pdfDoc = new Document(PageSize.A2, 10f, 10f, 10f, 0f);
            HTMLWorker htmlparser = new HTMLWorker(pdfDoc);
            PdfWriter.GetInstance(pdfDoc, Response.OutputStream);
            pdfDoc.Open();
            htmlparser.Parse(sr);
            pdfDoc.Close();
            Response.ContentType = "application/pdf";
            Response.AddHeader("content-disposition", "attachment;filename=Book1.pdf");
            Response.Cache.SetCacheability(HttpCacheability.NoCache);
            Response.Write(pdfDoc);
            Response.End();
        }
    }
}

public override void VerifyRenderingInServerForm(Control control)
{
}

I have done with this code , now it is getting opened by acrobat reader also.

protected void ExportToPDF(object sender, EventArgs e)
    {
        Response.ClearContent();
        Response.AddHeader("content-disposition", "attachment;filename=Book1.pdf");
        Response.ContentType = "application/pdf";
        Response.Cache.SetCacheability(HttpCacheability.NoCache);

        StringWriter sw = new StringWriter();
        HtmlTextWriter htm = new HtmlTextWriter(sw);

        Grid_Live.AllowPaging = false;
        Grid_Live.DataBind();
        this.ReadData();
        Grid_Live.RenderControl(htm);

        StringReader stringReader = new StringReader(sw.ToString());
        Document pdfDoc = new Document(PageSize.A4, 10f, 10f, 10f, 0f);
        HTMLWorker htmlWorker = new HTMLWorker(pdfDoc);
        PdfWriter.GetInstance(pdfDoc, Response.OutputStream);

        pdfDoc.Open();
        htmlWorker.Parse(stringReader);
        pdfDoc.Close();

        Response.Write(pdfDoc.ToString());
        Response.End();
    }

 previously also it was geting download but in opening it was giving error but with google docs it was opening only.