This paper studies the multiple-input multiple- output (MIMO) millimeter wave (mmWave) systems with non-linear power consumption model for 5G network. A new non-linear power consumption model is investigated, consisting of the power cost generated by the circuit and the non-linear power amplifiers. In this work, we aim to optimize the hybrid transceiver to maximize the system capacity subject to the resultant non-linear power constraint. In order to address this problem, we first transform the original optimization problem to a more tractable problem based on the weighted minimum mean squared error (WMMSE) approach. Then, we propose a novel transceiver design algorithm based on the penalty dual decomposition (PDD) optimization framework to address this problem. Moreover, a simplified algorithm is also proposed by using linear approximation. The effectiveness of the proposed algorithm is verified by simulation results.