In this paper, we design robust downlink beamforming against the imperfect channel state information (CSI) for beam division multiple access (BDMA) massive multiple-input multiple output (MIMO) systems. Following a worst-case deterministic model, the proposed design is formulated as minimizing the power consumption of base station (BS) under different signal-to-interference-plus-noise ratio (SINR) constraints. The S-Procedure and semi-definite relaxation (SDR) are used to convert the initial non-convex optimization to a convex semi-definite programming problem. Then the optimality of SDR is strictly proved by showing the rank-one property of the optimal beamforming thanks to the orthogonal channels under BDMA scheme. More importantly, we make one step further by deriving the optimal beamforming directions and optimal beamforming power allocation of the SDR in closed-form, which greatly reduces the optimization complexity and makes the proposed design practical for a real word massive MIMO system. Simulation results are then provided to verify the efficiency of the proposed robust beamforming algorithm.