This paper proposes a robust beamforming algorithm for massive multiple-input multiple-output (MIMO) low earth-orbit (LEO) satellite communications under uncertain channel conditions. Specifically, a Conditional Value at Risk (CVaR)-based stochastic optimization problem is formulated to optimize the hybrid digital and analog precoding aiming at maximizing the network data rate while considering the required Quality-of-Service (QoS) by each ground user. In particular, the CVaR is used as a risk measure of the downlink data rate to capture the high dynamic and random channel variations of the satellite network, achieving the required QoS under the worst-case scenario. Utilizing the decomposition and relaxation optimization techniques, an alternating optimization algorithm is developed to solve the formulated problem. Simulation results demonstrate the efficacy of the proposed approach in achieving the QoS requirements under uncertain satellite channel conditions.