Non-orthogonal multiple access (NOMA) in millimeter-wave (mmWave) multiple-input multiple-output (MIMO) (i.e., mmWave MIMO-NOMA) systems, is a promising technology to significantly enhance the spectrum efficiency of the fifth-generation (5G) mobile communication systems. Furthermore, enabling simultaneous wireless information and power transfer (SWIPT), where the energyconstrained user equipment (UE) equipped with power splitting receiver harvest both information and energy from the ambient radio-frequency (RF) signal, is crucial for energy-efficiency-maximization. In this paper, we initially design a user grouping algorithm, which preferentially groups UEs based on their channel correlation. Then, we design the analog RF precoder based on the selected user grouping for all beams, followed by a low-dimensional digital baseband precoder design, to further mitigate interbeam interference and maximize the achievable sum-rate for the considered system. Subsequently, we equivalently transform the original optimization problem into a joint power allocation and power splitting maximization problem. Then, we propose to decouple the joint power allocation and power splitting nonconvex optimization problem into four separate optimization problems and then solved iteratively via an alternating optimization (AO) algorithm. Simulation results show that high spectrum and energy efficiency can be realized with the proposed algorithms than those of state-of-the-art designs and the conventional SWIPT-enabled mmWave MIMO-OMA system. INDEX TERMS SWIPT, Millimeter wave communication, MIMO, NOMA, hybrid analog-digital precoding, multiuser channels, optimal scheduling, power splitting, optimization methods.