This paper proposes four control strategies for Z-source matrix converter: simple maximum boost control, maximum boost control, maximum gain control and hybrid minimum stress control. The maximum gain control can obtain the maximum gain at the same modulation index among all four; and the hybrid minimum voltage stress control can obtain the minimum voltage stress at the same voltage gain. The relationship of voltage gain to modulation index and the relationship of voltage stress to voltage gain have been analyzed in detail for each method and verified by simulation and experiments.