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In this paper, the system performance of a hybrid time–power splitting relaying (TPSR) two-way half-duplex (HD) relaying network over a Rayleigh fading channel is investigated in terms of the outage probability (OP) and intercept probability (IP). The proposed model has two sources, A and B, which communicate with each other with the help of an intermediate relay (R) under the presence of an eavesdropper (E). The physical layer security (PLS) was considered in this case. Firstly, we derived the closed-form expressions of the exact and asymptotic IP in two cases, using MRC (maximal ratio combining) and SC (selection combining) techniques. The closed-form expressions of the system OP was then analyzed and derived. All the analytical expressions of the OP and IP of the system model were verified by a Monte Carlo simulation in connection with all the main system parameters. In the research results, the analytical and simulation values were in total agreement, demonstrating the correctness of the system performance analysis.