Is it possible to POST request data from browser to server in compressed format? If yes, How can we do that?
The server->client responses can be gzip compressed automagically by the server.
Compressing the client->server messages is not standard, so will require some work by you. Take your very large POST data and compress it client-side, using JavaScript. Then decompress it manually on the server side.
This will usually not be a beneficial thing to do unless your bandwidth usage is a major bottleneck. Compression requires both time and CPU usage to perform.
Compressing data sent from the browser to the server is not natively supported in the browsers.
You'll have to find a workaround, using a clientside language (maybe a JavaScript GZip implementation, or a Java Applet, or ...). Be sure to visually display to the user what the browser is doing and why it is taking some time.
I don't know the scope of your application, but on company websites you could just restrict input to compressed files. Ask your users to upload .zip/.7z/.rar/... files.