This paper investigates the system performance of hybrid time-power switching based relaying (TPSR) energy harvesting enabled in the multi-source half-duplex relaying network over the Rayleigh fading channel. The outage probability (OP) of the proposed system model with implementing maximal ratio combining (MRC) and selection combination (SC) technique at the receiver is presented and analyzed. The impact of main system parameters, such as transmit signal to noise ratio (SNR), time fraction factor, power fraction factor, and number of sources, on the system performance is analyzed. The results indicate that the performance of the system in the case of MRC is more improved than in the SC case. It shows the benefit of MRC for optimizing SNR at the receiver. Furthermore, we recognize that there exists an optimal value of time fraction factors where the system performance obtains the best performance. Finally, the correctness of the analytical formulation is verified by Monte Carlo simulation.