This letter proposes a low-complexity deep-learning-based direction-of-arrival (DOA) estimation method for a hybrid massive multiple-input multiple-output (MIMO) system with a uniform circular array at the base station. In the proposed method, we first input the received signal vector into some small deep feedforward networks that are trained offline. Based on the outputs of the networks, we then generate a set of candidate angles. By selecting the optimal one from all candidate angles, we finally obtain the DOA estimation. Simulation results demonstrate that, compared with the conventional maximum likelihood (ML) method, the proposed DOA estimation method can achieve similar or even better performance with much less complexity.