Relay transmission can enhance a communication reliability, increase a transmission rate and save power at a sending station in wireless networks. The scenario under consideration is a simple relay system that sending station sends coded data to a receiving station through a relay station. The relay station makes hard decision and transmits it. The receiving station decodes the error-correcting-coded bits using loglikelihood ratio (LLR). Here, it is important to set initial LLR to decode the coded data accurately at the receiving station. In this paper, we present how to set initial LLR for belief propagation decoding in the relay system to achieve better decoding error rate performances. We calculate initial LLR based not only on the channel from the relay station to the receiving station, but also on the channel from the sending station to the relay station when the station decodes error-correcting coded data. When we use turbo code or low-density parity-check (LDPC) code as error-correcting code, we decode the coded data accurately by the use of accurate initial LLR. Through computer simulation, we showed that the proposed method achieves better error rate performances compared to the conventional method both when the channel estimation is perfect and when the channels are estimated. Moreover, we showed that the average number of decoding iterations of the proposed method decreases compared to those of the conventional method.