By using the analysis of phase, fixed point and tunneling rate between two wells, we study the nonlinear Landau-Zener transition of Fermi superfluid gases in a two-mode system. We find that the interaction between fermi pairs can affect the quantum transition. We also find that when the interaction parameter c is less than the critical value c*, in the adiabatic limit, the quantum adiabatic transition theorem is still satisfied, but when the interaction parameter c is greater than this critical value, the quantum adiabatic transition theorem will not be satisfied. Finally, we obtain the relationship between the tunneling rate and the scan rate by comparing with the linear case.