Currently, the Z-source network is applied in matrix converters (MCs) to address the low voltage transfer ratio (VTR) issue of MCs. A novel structure of the Z-source ultra-sparse matrix converter (ZSUSMC)is proposed by integrating the Z-source network with the ultra-sparse matrix converter. This structure inserts the Z-source network between the rectification stage and the inversion stage of the ultra-sparse matrix converter. Additionally, two space vector modulation (SVM) methods which is improved zero-vector and non-zero-vector are analyzed and compared in the rectification stage, along with their respective advantages and disadvantages. Furthermore, to reduce output harmonic content and the number of switching state transitions, a new switching transition mode is proposed to minimize switching state changes throughout the entire switching cycle. Finally, the ZSUSMC modulation method is analyzed through software simulation and hardware experiments. The results demonstrate that the ZSUSMC can improve the voltage transfer ratio, with each modulation method having its own characteristics. Moreover, the new switching transition mode enhances the output power quality.