I have an url link of this video from Cowboy Bebop, I have seen it many times, but I just interested and chill with the piano play at the soundtrack.Is Anyone know what is the genre of jazz or music style of that elite soundtrack?
It's just a piano/violin duet from the sounds of it. I wouldn't classify this as jazz necessarily. It sounds like a movie score more than a 'genre' in my opinion. 'Smooth Jazz' would be your best bet, it isn't quite 'Cool Jazz'.