We propose a new group shuffled belief propagation (BP) decoding algorithm for low-density parity check (LDPC) code. In our method, the variable nodes (VNs) will be re-grouped in each iteration. First, we decide if each message sent from a VN to a check node (CN) is reliable. Then, we further identify the CN which can provide reliable information. Based on the filtering of the reliable messages, we select the VNs which are able to obtain most reliable messages in to a group. After VN updating, the above procedure will be re-performed until all VNs are updated in one iteration. Numerical results show that the proposed shuffled BP decoding outperforms the existing shuffled BP decoders for LDPC codes and performance improvements become more distinctive at higher rate.