Millimeter wave (mmWave) communications have been considered as a key technology for future 5G wireless networks. In order to overcome the severe propagation loss of mmWave channel, mmWave multiple-input multiple-output (MIMO) systems with analog/digital hybrid precoding and combining transceiver architecture have been widely considered. However, physical layer security (PLS) in mmWave MIMO systems and the secure hybrid beamformer design have not been well investigated. In this paper, we consider the problem of hybrid precoder and combiner design for secure transmission in mmWave MIMO systems in order to protect the legitimate transmission from eavesdropping. When eavesdropper's channel state information (CSI) is known, we first propose a joint analog precoder and combiner design algorithm which can prevent the information leakage to the eavesdropper. Then, the digital precoder and combiner are computed based on the obtained effective baseband channel to further maximize the secrecy rate. Next, if prior knowledge of the eavesdropper's CSI is unavailable, we develop an artificial noise (AN)-based hybrid beamforming approach, which can jam eavesdropper's reception while maintaining the quality-of-service (QoS) of intended receiver at the pre-specified level. Simulation results demonstrate that our proposed algorithms offer significant secrecy performance improvement compared with other hybrid beamforming algorithms.