Hybrid precoding (HP) techniques based on partially connected structure (PCS) are widely studied in millimeter-wave (mmWave) MIMO communication systems due to low hardware cost as well as low energy consumption. Many efficient HP schemes based on PCS have recently been proposed, which require that the baseband precoding (BP) matrix of the digital domain to be a diagonal or square matrix. To avoid the interference from multiple streams of a single-user, the number of data streams for a single-user should not exceed the rank of the equivalent baseband MIMO channel (EBMC) before BP. Hence, these schemes are only reliable to the case that the EBMC matrix is full rank. However, the EBMC matrix may be rank-deficient due to the geometrical change and misplacement of the transceiver in practice. In this paper, we focus on the HP with PCS and propose a family of effective iterative matrix factorization (IMF) algorithms for HP designs, which are suitable for rank-deficient EBMC. We firstly propose an IMF-HP algorithm based on traditional design, which approximates the performance of the fully digital precoder by utilizing an alternate optimization strategy. In particular, we present a successive interference cancelation combined with IMF for HP design (SiC-IMF-HP) to further achieve higher throughput and lower complexity. Simulation results show that the proposed SiC-IMF-HP algorithm performs better than other recently proposed hybrid precoding schemes based on PCS when the number of data streams equals to the number of RF chains. The proposed algorithms both enjoy an acceptable computational complexity.