Abstract: In small step simulation, power electronic converters often use the L/C-based fixed-admittance model, which has shortcomings such as complicated parameter setting, high virtual power loss, and the large gap of characteristics between the model and the ideal model. In view of this situation, this paper proposed a parameterized fixed-admittance model for power electronic converters based on cross initialization. In different operating states of converters, switches adopted the fixed-admittance model with the parameterized history current source. The steady-state characteristics and transient convergence characteristics were determined by the parameters of the historical current source, and the parameter setting was decoupled from external circuits. Besides, the initial error of state switching was reduced by cross initialization, which is the mutual-initialization method of switches in the same bridge arm during state switching, and virtual power loss of the model was eliminated. The simulation results demonstrate that this model has the same efficiency and higher accuracy compared with the traditional constant admittance model. Furthermore, its operating characteristics are closer to the ideal model.