I'm very much new to chrome app development, for my application I need to run a web-server which will start as my app launch and will be close with closing of my app. I like to use web-server-for-chrome plugin as my web-server but is there any way to start and stop a server from inside chrome app?
Sure, you would need to use chrome.sockets.tcpServer api, it allows you to create server applications using TCP connections.
And for examples, take a look at chrome-app-samples-webserver.