Theoretical investigation of the online algorithms has received considerable attention recently. The previous generalization bounds of online learning algorithms are usually established on the base of independent and identically distributed (i.i.d.) samples. In this paper, we go far beyond this classical framework to investigate the generalization ability of online algorithm with $\alpha$-mixing sequence. We define $\alpha$-mixing sequence by using the total variation, and our analysis requires only martingale convergence arguments. At last, ``regret" is utilized to measure the performance of online algorithms. Our main result is a tighter generalization error estimation than that of $\beta$-mixing sequence.