How to improve written and verbal communication skills? Watch
Can someone please suggest me some ways of improving English and communication skills.
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Based on your post, your English is not that bad
However, the best way to improve is... to practice, practice and practice some more! You will improve your written communication through uni assignments and by reading as many books in English as possible.
To improve your spoken English, it might be a good idea to join some societies. You'll get the chance to make new friends, do something that you enjoy and more importantly... socialize, in English. There are other things you can do, like watch movies without subtitles or try to use English subtitles. When you listen to music, try to listen to the words. Google Translate and dictionaries are good tools that will help you improve. Another thing you can do is to read out loud, hearing yourself read will help you spot your mistakes better.
And for spoken English, I really wouldn't worry - just get on with making friends, going to the shops, watching TV etc. and you'll have seen improvements before you know it!