Whether English is your native language or not, it can never hurt to improve your writing skills. Fortunately, you don't have to do too much in order to see an improvement.
Top Tips for Improving your Writing in English
Read. It's surprising how much you pick up without realising it. This is probably the best thing you can do to improve your writing, and is suggested by teachers of English as a second language and famous novelists alike. Try and stretch yourself by reading books that are slightly more difficult than you're used to. For example, if you like horror stories, try reading classic Gothic novels like Dracula or Frankenstein (you might want to avoid The Castle of Otranto, though, because that's an endurance test for anyone).
Get feedback on your writing. Most teachers are happy to help students who show a genuine desire to learn and improve their writing. If it's academic writing that you're worried about, try writing practice essays (you don't even have to write whole ones; a good paragraph now and then will be enough) and ask a teacher to look over them with you.
Don't be afraid to ask for guidance. If you don't understand why a sentence is wrong, it's best to ask and have it explained to you. This way, you'll be able to improve on it for next time.
Take regular breaks from learning. Not only does this help your brain to absorb the information and improve concentration, but it also stops the work seeming so daunting. It can be easy to feel overwhelmed by something if you approach it all in one go.
Be patient. Improving your English writing is a gradual process, so don't worry if you don't notice the results right away. Keep at it, and don't give up!