To enable multi-stream transmission and increase the achievable rate, a hybrid digital/analog precoding structure is usually adopted in millimeter-wave (mmWave) MIMO systems. However, it may require matrix operations with a scale of antenna size, which is generally large in mmWave communications. Moreover, the channel estimation is also rather time-consuming due to the large number of antennas at both Tx/Rx sides. In this paper, a low-complexity overall channel estimation and hybrid precoding approach is proposed. In the channel estimation phase, a hierarchical multi-beam search scheme is proposed to fast acquire $N_{\mathrm {S}}$ (the number of streams) multipath components (MPCs)/clusters with the highest powers. In the hybrid precoding phase, the analog and digital precodings are decoupled. The analog precoding is designed to steer along the $N_{\mathrm {S}}$ acquired MPCs/clusters at both Tx/Rx sides, shaping an $N_{\mathrm {S}}\times N_{\mathrm {S}}$ baseband effective channel, while the digital precoding is performed in the baseband with the reduced-scale effective channel. Performance evaluations show that, compared with the state-of-the-art scheme, while achieving a close or even better performance when the number of radio frequency chains or streams is small, both the time complexity of the channel estimation and the computational complexity of the hybrid precoding are reduced.