The below code will do so
Public Shared Sub CompressFile(filePath As String)
Dim info As New FileInfo(filePath)
Using originalFileStream As FileStream = info.OpenRead()
Using compressedFileStream As FileStream = File.Create(filePath & Convert.ToString(".gz"))
Using compressionStream As New GZipStream(compressedFileStream, CompressionMode.Compress)
originalFileStream.CopyTo(compressionStream)
End Using
End Using
End Using
End Sub