In this paper, we propose a new belief propagation (BP) decoding algorithm for a fast convergence decoding of regular LDPe codes. The fast convergence is achieved by grouping and scheduling updates of nodes on bipartite-graph without additional computations or approximations. For this reason, the proposed algOrithm can be applied to serially constructed decoder, and can reduce power consumption and decoding delay of the decoder. The simulation results show that the convergence speed of the proposed algorithm dependS on the degree of variable-nodes dv of bipartite-graph, and the average number of iterations of the decoder can be reduced to (dv - l)/dv by using the proposed algorithm without performance degradations and additional computations.