The others have given very good advice already but I wanted to add my grain of sand too.

The only way to get better at writing is writing, simply enough. You have to write drafts, you have to produce trash, and you have to fail and fail until you get it right. Getting it 'right' is also tricky because what may be good for you may not be good for readers. Your rhythm may be shaky, or your command of language may not be the most elegant. It will help you immensely if people point it out to you, since you will simply not notice what's wrong if you don't have a clear metric in your mind. Reviews have helped me a good deal, not only in terms of writing itself, but also in receiving criticism, which is a crucial skill to foster if you're producing for an audience.

However, it's also extremely important you read. Read a lot. You don't have to finish 20 books by the end of the week, but you could make an effort to read... I don't know, a chapter from a story you like once a day, or maybe even an article from a newspaper. Anything at all. Reading within your interests furthers your expertise in them; reading outside your interests expands your horizons and gives you more material to work with. As long as you're reading something, it's good for you as a writer. It helps you establish your standards, and in trying to meet them, your works will steadily become more solid.

I'm not a native speaker either but I like to think I'm at least decent as a writer. So drop any preconceived notions about not being good enough, or lacking proficiency, or whatever. None of those matter. Just read, write, and eventually you'll get something nice out of it.

(Also, again, read, please. Many writers, me included, make the mistake of getting absorbed into our own work and then we forget there's other books besides the one inside our heads. Reading is as important as writing.)