This paper presents a motor drive system based on the quasi-Z source inverter (qZSI) to control the pole-phase modulation (PPM) machines. With the inductor-capacitor (LC) impedance network, the qZSI can advantageously use the shoot-through state to obtain any desired output ac voltage. In this paper, the capacitor voltage of the quasi-Z source (qZS) network is controlled to obtain the constant dc-link peak voltage. The double vector control algorithms are developed for the PPM induction machine (IM), where one for 3-phase with 12-pole mode, and another for 9-phase with 4-pole mode. The drive system, including the PPM-IM model and the proposed control scheme, is built in MATLAB/ SIMULINK. Three operating modes of the system, i.e., 3-phase with 12-pole, 9-phase with 4-pole, and pole-changing transient process are tested in the simulations. Simulated results verify the proposed drive system.