You can follow this link
http://msdn.microsoft.com/en-us/library/system.io.compression.gzipstream(v=vs.90).aspx
public static void Compress(FileInfo fi)
{
// Get the stream of the source file.
using (FileStream inFile = fi.OpenRead())
{
// Prevent compressing hidden and already compressed files.
if ((File.GetAttributes(fi.FullName) & FileAttributes.Hidden)
!= FileAttributes.Hidden & fi.Extension != ".gz")
{
// Create the compressed file.
using (FileStream outFile = File.Create(fi.FullName + ".gz"))
{
using (GZipStream Compress = new GZipStream(outFile,
CompressionMode.Compress))
{
// Copy the source file into the compression stream.
byte[] buffer = new byte[4096];
int numRead;
while ((numRead = inFile.Read(buffer, 0, buffer.Length)) != 0)
{
Compress.Write(buffer, 0, numRead);
}
Console.WriteLine("Compressed {0} from {1} to {2} bytes.",
fi.Name, fi.Length.ToString(), outFile.Length.ToString());
}
}
}
}
}