It is difficult to implement a fully digital precoding in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, owing to the huge cost and power consumption of radio frequency (RF) chains. Hybrid precoding that uses the combination of analog beamforming, together with digital precoding, offers a feasible solution to this problem where far lesser number of RF chains are employed compared to the number of antennas. We consider a downlink multi-user massive MIMO scenario and propose a hybrid precoding scheme that maximizes signal-to-leakage-and-noise ratio (SLNR). Each mobile station (MS) determines its analog combiner first and then the base station (BS) constructs the analog beamformer and the digital precoder of the hybrid precoder in two separate stages to maximize the SLNR for each user. We show, through simulations, that the proposed hybrid SLNR-based precoder exhibits a performance close to the fully digital SLNR-based precoder despite using only a few number of RF chains.