Aiming at poor system performance in existing partially connected hybrid precoding schemes, in this paper, we propose a partially connected hybrid precoding scheme based on alternating optimization with the auxiliary precoder. In particular, the spectral efficiency optimization problem is transformed into a sub-optimization problem under certain constraints. For each sub-optimization problem, we use the singular value decomposition method to optimize the analog precoder and digital precoder alternately, and optimal solutions are provided for both digital and analog precoders in each alternate iteration. Moreover, we design a heuristic algorithm to calculate the initial analog precoder as the starting point for alternating optimization, which speeds up the convergence speed. The simulation results show that the proposed algorithm is at least 16.2% higher than the existing two traditional partially connected algorithms at 20 dB received SNR with almost no increase in complexity.