BGP (Border Gateway Protocol) as a kind of mature routing protocols, has been widely applied in all kinds of largescale network. With regard to routing protocol, the important problem is the convergence time, which is an important index to evaluate the availability and robustness of network. This paper analyzes the network convergence problem, elaborates the method of accelerating network convergence of BGP, and apply it to an example. Experimental results prove that the improved Minimum Route Advertisement Interval (MRAI) not only guarantee network stability and robustness but also accelerate the routing convergence time.