To prolong the lifetime of energy-constrained cooperative networks, radio frequency energy harvesting (RFEH) technology can effectively solve the energy constraints of nodes batteries, and we consider the maximum ratio combining (MRC) method at the destination node to improve the reliability of the link transmission. Thus, we propose the power splitting-based double-relay cooperative transmission (PSDRCT) protocol with RFEH in the decode-and-forward (DF) mode in this study. According to the transmission process of the proposed protocol, the analytical expressions of outage probability, throughput, and energy efficiency are obtained. Numerical simulation results demonstrate that the location of the relay nodes, power allocation ratio, energy conversion efficiency, and transmission power are the key factors affecting the performance of the protocol. In addition, the proposed protocol has lower outage probability than the time switching-based double-relay cooperative transmission (TSDRCT) protocol under the same power allocation ratio and energy conversion efficiency.