Abstract Wireless multiple-input multiple-output (MIMO) two-way relay systems have received increasing attention recently. In a simple two-hop relay system, physical-layer network coding (PNC) is an effective scheme for relay to map the transmitted symbols from two terminal nodes into the network coded symbol. This paper considers a two-hop two-way relay system which uses the Alamouti space-time code for signaling between all nodes and channel quantization for PNC mapping at the relay. Specifically, based on the concept of CQ-PNC we derive a PNC mapping rule for two pairs of network coded symbols. An adaptive mapping scheme based on minimum residual interference power is introduced to reduce the effect of quantization error. Finally, a relay selection method based on minimum residual interference power is proposed as a means to increase the system performance.