How can I improve music composing skills for all type's of music?

First, study the basics. Second listen to different types of music. Third, apply what you learned in what you hear. Fourth, study the music that you listen to. once you've done this, you will learn the progression that each song uses and you will be able to apply this in your music writing skills.

Study, listen, practice and compose. There's an online composer's website that's free - It's called SongU and you compose stuff, upload and other's listen and give you constructive criticism.