Hybrid architecture is a promising candidate precoding scheme to balance the achievable spectral efficiency and power consumption in millimeter wave multiple input multiple output systems. A practical partially dynamic subarray-connected architecture is developed to improve the transmission performance. In this proposed architecture, the set of antennas in each subarray is fixed, but the subarrays connected to each radio frequency chain are dynamic. Moreover, we study how to optimize jointly the partially dynamic subarray structure and the hybrid precoders under the constraints of total transmit power and hardware limitation. This joint optimization problem is divided into two sub-problems. For the first sub-problem, a low-complexity algorithm is proposed to determine the partition of subarrays using the long-term spatial channel covariance. Then, the penalty decomposition method is adopted to design the hybrid precoders. Numerical results verify that the partially dynamic subarray design algorithm offers one or two orders of computation time saving compared with the existing algorithms, and the hybrid precoding algorithm outperforms the existing algorithms in terms of spectral efficiency. Moreover, compared with the fully dynamic subarray structure adopted in the existing algorithms, the proposed structure achieves spectral efficiency gain and energy efficiency gain using less hardware.