An axisymmetric and parameterized finite element model for the shrink disc connection of a wind turbine gearbox was established. And the torque from the shaft was taken into consideration and the non-linear finite contact software ANSYS was used to analyze the model's strength. As material properties, processing tolerance, boundary conditions and loading, etc. affect the accuracy of analysis, we used PDS module in ANSYS and based on structure failure mode to determine the structure function, and then set up a structure limit state equation. The reliability of the shrink disc connection was calculated with Latin hypercube sampling of Monte Carlo method, and its reliability, failure probability and cumulative distribution were obtained. The results indicate that the transmission torque and the strength of components meet design requirements and the reliability of the connection reaches 94.8%. It's hoped to provide some references for the design of shrink discs in wind turbine gearboxes.