Perhaps you are speaking word-by-word, or almost.
I mean, chances are that you speak slowly and then you have time to think of your own accent. That is, then your accent shows.
Practice makes perfect, don´t get anxious to get perfection quickly, Rome wasn´t built in a day! Try watching interviews, movies, listening radio, and try to emulate something you have just listened to. Sentences etc. It´s my advice, I am no teacher, so more useful comments might come.
Other thing that comes to mind, is that you may be overly self-concious of your accent, or of you talking, chill out and maybe you may improve your talking, if that is/was a factor.