Beamspace multiple-input multiple-output (MIMO) systems leverage the lens antenna array to reduce their hardware cost, which is a promising technology in millimeter wave (mmWave) frequency bands. This letter proposes a novel signal-to-leakage-plus-noise ratio (SLNR)-based beamspace precoding and beam selection scheme to improve the downlink sum rate (SR) of the beamspace mmWave massive MIMO channels. First, for a given beam subset, a SLNR maximization-based beamspace precoder is designed to mitigate the inter-user interference caused by leakage power, thus enhancing the SR. Then, an approximated expression of the SR is formulated, based on which an iterative radio frequency (RF) precoding and beam selection method is designed to further improve the system SR. Numerical results demonstrate a superior SR performance of the proposed scheme over state-of-the-art methods.