I think I've been in the exact same position as you, Zhennie. What I did was continue dancing with my (now former) partner and look for another one in the meantime. It didn't take me very long, but that was because I had a BIG variety of choice (which I wasn't aware of at the time, so I was very frustrated and started wondering if maybe it was better to continue without partner, like you).
A lot of people told me not to dump him, a lot of people told me to look for another partner. Opinions vary, BUT if you feel that you can handle to dance like this for a little while longer, I shouldn't dump him (yet) and just look for another partner in the meantime. If you feel that you can't bear the situation anymore, dump him and continue dancing with your teacher (like Joy Kelley said) for the time being.
Whatever you do, DO address the situation to your partner and tell him what bothers you. Give him a chance to work on his dancing! Also, if that didn't help, always be open to a new partnership, who knows, maybe the right one will come dancing your way very soon 
"Carpe diem, quam minimum credula postero." - Horace