In this paper, we propose a new fast convergence scheme of the BP (belief propagation)-decoding algorithm for regular-LDPC decoder. The properties of fast convergence in the BP-decoding algorithm are derived from the scheduling updates of check-node in the bipartite-graph without additional computations or approximations. For this reason, the decoder using proposed scheme might be constructed by serial constructions and can reduce the power consumption and decoding delay. The convergence speed depends on the degree of bit-node j, and the number iterations of the decoder can be reduced to (j-1)/j by using the proposed scheme without performance degradations. We analyze the efficiency and performance of the proposed scheme by applying to (3,6)regular-LDPC codes on AWGN channel.