Previous studies revealed that low-density parity-check convolutional codes (LDPC-CC) with rational parity-check matrices may outperform LDPC-CC with ordinary polynomial parity-check matrices. However, such a performance improvement relies on a dynamic scheduling-aided decoding scheme with high processing latency which may prevent LDPC-CC with rational parity-check matrices from practical applications. In this paper, we find that conventional belief-propagation algorithms suitable for high-speed parallel implementation can still provide the satisfactory performance gain for LDPC-CC with rational parity-check matrices as long as some virtual channel outputs which can accelerate the convergence of iterative decoding are properly supplied. Criteria for generating virtual channel outputs are investigated from the viewpoint of Tanner graph. Simulation results are also provided for performance verification.