Spontaneous dynamic‐rupture simulation in 3D is a difficult task in seismology, especially for the rupture dynamics of a fault with complex geometry and a free surface. In this study, we model an irregular fault that reaches the free surface and investigate the rupture dynamics of the intersection between the earthquake‐induced fault and the Earth’s surface. We use the recently proposed curved grid finite‐difference method (CG‐FDM) to simulate a spontaneous dynamic rupture. However, this involves solving the inversion of an ill‐conditioned matrix that is required in finite‐difference method modeling at the point of intersection, which must be addressed to achieve stable simulation conditions. We achieve stable conditions at the intersection between the fault plane and the free surface by considering the continuity of the fault’s normal displacement, ensuring that the point of intersection meets the conditions of both the fault and the free surface. To verify our method, we simulate the spontaneous dynamic rupture of a rough fault in half‐space and compare the results with those from another method. The good agreement between two methods validates our mathematical strategy for modeling the intersection between an irregular fault plane and a free surface using CG‐FDM.