To avoid collisions and ensure driving safety, comfort, and efficiency, in this study, we propose a trajectory planning strategy for intelligent vehicles navigating curvy road scenarios. This strategy is based on a dynamic spatio-temporal corridor search. First, an obstacle space expansion module is constructed using a critical safety distance model to generate a searchable spatio-temporal corridor. Next, a dynamic step expansion is performed to improve the traditional hybrid A* search algorithm by the discretization of front-wheel steering angles and acceleration. The bisection method is applied to iteratively optimize the child nodes at each step, and the child node with the lowest cost is selected as the rough search node. Subsequently, a locally weighted dual-regression fitting algorithm is employed for segment trajectory fitting, and the optimal trajectory is generated. Finally, the performance of the proposed trajectory planning strategy is validated on the Carla simulation platform. The results show the effectiveness and efficiency of our strategy in three typical scenarios.