Hybrid analog/digital precoding in millimeter-wave (mmWave) multi-input multi-ouput (MIMO) systems is capable of achieving the near-optimal full-digital performance at reduced hardware cost and power consumption compared to its full-RF digital counterpart. However, having numerous phase shifters is still costly, especially when the phase shifters are of high resolution. In this paper, we propose a novel twin-resolution phase-shifter network for mmWave MIMO systems, which reduces the power consumption of an entirely high-resolution network, whilst mitigating the severe array gain reduction of an entirely low-resolution network. The connections between the twin phase shifters having different resolutions and the antennas are either fixed or dynamically configured. In the latter, we jointly design the phase-shifter network and the hybrid precoding matrix, where the phase of each entry in the analog precoding matrix can be dynamically designed according to the required resolution. This method is slightly modified for the fixed network's hybrid precoding matrix. Furthermore, we extend the proposed method to multi-user MIMO systems and provide its performance analysis. Our simulation results show that the proposed dynamic hybrid precoding method strikes an attractive performance vs. power consumption trade-off.