string strInfileName = @"D:\test.txt";
string strOutfileName = @"D:\test.zip";
FileStream fsInfile = new FileStream(strInfileName, FileMode.Open);
byte[] buff = new byte[(int)fsInfile.Length];
fsInfile.Read(buff, 0, buff.Length);
fsInfile.Close();
FileStream fsOutfile = new FileStream(strOutfileName, FileMode.Create);
GZipStream gzStream = new GZipStream(fsOutfile, CompressionMode.Compress, true);
gzStream.Write(buff, 0, buff.Length);
gzStream.Close();
fsOutfile.Close();

using (FileStream inStream = new FileStream("", FileMode.Open))
using (FileStream outStream = new FileStream("", FileMode.OpenOrCreate))
using (GZipStream gzipStream = new GZipStream(outStream, CompressionMode.Compress))
{
    inStream.CopyTo(gzipStream);
    //.net4 以前就读一部份，写一部分，直到完成。
}

------解决方案--------------------
VB.NET code

   Private Shared Sub exeCompress(ByVal orgStream As System.IO.Stream, ByVal cmpStream As System.IO.Stream)
  Dim zipStream As System.IO.Compression.GZipStream = New System.IO.Compression.GZipStream(cmpStream, System.IO.Compression.CompressionMode.Compress)
        Dim buffer As Byte() = New Byte(1024) {}
        While True
            Dim bytesRead As Integer = orgStream.Read(buffer, 0, 1024)
            If bytesRead = 0 Then
                Exit While
            End If
            zipStream.Write(buffer, 0, bytesRead)
        End While
        zipStream.Flush()
        zipStream.Close()
    End Sub