This article investigates beam alignment for multi-user millimeter wave (mmWave) massive multi-input multi-output system. Unlike the existing works using machine learning (ML), an alignment method with partial beams using ML (AMPBML) is proposed without any prior knowledge such as user location information. The neural network (NN) for the AMPBML is trained offline using simulated environments according to the mmWave channel model and is then deployed online to predict the beam distribution vector using partial beams. Afterwards, the beams for all users are all aligned simultaneously based on the indices of the dominant entries of the obtained beam distribution vector. Simulation results demonstrate that the AMPBML outperforms the existing methods, including the adaptive compressed sensing, hierarchical search, and multi-path decomposition and recovery, in terms of the total training time slots and the spectral efficiency.