Intersections are high-risk locations for traffic conflicts, where coordinating autonomous vehicles (AVs) with vulnerable road users (VRUs) like pedestrians is critical for safety. To ensure VRU crossing safety and traffic efficiency at intersections, this study proposes a Directional-improved Rapidly-exploring Random Tree (D-RRT) trajectory optimization algorithm based on VRU trajectory prediction. Using the self-collected Weiyang Road Video Dataset (WY-Road Dataset) and the Dalian University of Technology Video Dataset (DUT Dataset), we first identify motion features influencing trajectory prediction, then mathematically model intersection scenarios with constraints. Safety distance models are established for categorized VRU-vehicle interaction scenarios. The proposed D-RRT algorithm improves conventional RRT through directional optimization, with trajectories further refined via cubic spline interpolation. Results demonstrate that compared to RRT, D-RRT reduces trajectory curvature variation by 31.67%, shortens average planning time by 0.1s with better temporal stability. Additionally, the D-RRT algorithm excels in increasing the minimum distance to VRUs and reducing the risk of VRU-vehicle conflicts, ensuring the quality of trajectory optimization.