This paper proposes low complexity soft decoding for physical layer network coding with coded modulation that can be applied to bi-directional relay systems with quadrature amplitude modulations (QAMs). Although the received signal at the relay is superposition of the two transmission signals from the terminals in the systems, the signal detection and the channel decoding can be carried out by the proposed decoding with low computational complexity, because the proposed soft decoding can generates the soft input signal with the use of the region detection. The proposed decoding achieves a soft decoding gain without the prohibitive exhaustive search. The proposed decoding can keep the complexity even when higher order QAMs are applied. The performance of the proposed soft decoding is evaluated by computer simulation in a two hop MIMO-OFDM bi-directional relay system. The proposed decoding attains a soft decoding gain of about 2.0dB at the BER of 10-5 in spite of cardinality of QAMs.