In this paper, we investigate a dual-hop simultaneous wireless information and power transfer (SWIPT) based amplifying-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system where the relay node harvests energy based on radio frequency (RF) signals transmitted from the source node through the hybridized power-time splitting-based relaying (HPTSR) protocol to forward information to the destination node. The joint optimization of the time-switching (TS) factor, source and relay precoding matrices, and the power-splitting (PS) ratio vector is proposed to maximize the mutual information (MI) between the source and destination nodes. We derive the optimal structure for the source and relay precoding matrices to simplify the transceiver optimization problem. Two algorithms based on the upper bound and lower bound of the objective function are proposed to efficiently solve the optimization problem with low computational complexity. Numerical examples demonstrate that the proposed algorithms provide a better MI performance compared with TS based and PS based energy harvesting (EH) relay systems. INDEX TERMS Amplify-and-forward (AF) relay, energy harvesting, hybridized power-time switching relaying (HPTSR), multiple-input multiple-output (MIMO) relay, simultaneous wireless information and power transfer (SWIPT)