When finite set model predictive control is applied to an O-Z-source inverter(O-ZSI) containing a transformer, there are multiple control variables, it is difficult to adjust the weighting factors, and the currents on both sides of the transformer could change abruptly, making it impossible to calculate and derive reference values to directly predict and control the currents on both sides of the transformer. In this paper, an improved sequential-model predictive control is proposed for O-ZSI with a transformer without adjusting the weighting factors. By equating the transformer as a parallel connection of the excitation inductance with a set of ideal transformers without adjusting the weighting factors, the reference value of the magnetization current of the excitation inductance can be calculated according to the theoretical derivation, which can realize the predictive control of the O-ZSI. Simulation analysis and experimental results show that the proposed control method achieves the sequential-model predictive control of O-ZSI without adjusting the weight factors, with good steady-state and dynamic characteristics.