In the mmWave communication network, exhaustive beam search (EBS) assisted beam training is suggested for accurate beam alignment between the access point (AP) and the user equipment (UE) in the existing 3GPP standard. Nevertheless, the EBS method suffers from unacceptable training overheads, which may degrade the network throughput, especially when the beam space is large. In this paper, we propose an intelligent multi-peak beam training algorithm to tackle this issue. The main idea of the algorithm lies in, by applying binary encoding into the narrow beam index, several multi-peak wide beams can be constructed. Then, a deep neural network (DNN) is carefully designed and trained to decode the probed signal-to-noise ratios (SNRs) of multi-peak wide beams into the optimal narrow beam index. With the well-trained DNN, the optimal narrow beam can be identified online by feeding the probed SNRs of the multi-peak wide beams into the DNN. Simulation results show that the proposed algorithm outperforms the state of the arts in terms of overheads and throughput.