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Physical-layer Network Coding (PNC) has shown its power for improving the throughput effectively of the bi-directional relay system. Most of the existing PNC schemes are carried out under the assumption of perfect synchronization. In this paper, we provide some new insights into the joint design of Low-Density Parity-Check (LDPC)-coded and PNC for asynchronous bi-directional relay system with BPSK signaling. In particular, a novel LDPC and PNC joint design method is proposed for mitigating the performance degradation caused by the different timing offsets between relay and two source nodes. Simulation results show that the proposed joint design of LDPC and PNC scheme outperforms traditional method for bi-directional relay system in the presence of insufficient timing synchronization.