Trajectory planning is of vital importance to decision-making for autonomous vehicles. Currently, there are three popular classes of cost-based trajectory planning methods – sampling-based, graph-search-based, and optimization-based. However, each of them has its own shortcomings, for example, high computational expense for sampling-based methods, low resolution for graph-search-based methods, and lack of global awareness for optimization-based methods. It leads to one of the challenges for trajectory planning for autonomous vehicles, which is improving planning efficiency while guaranteeing model feasibility. Therefore, this paper proposes a hybrid planning framework composed of two modules, which preserves the strength of both graph-search-based methods and optimization-based methods, thus enabling faster and smoother spatio-temporal trajectory planning in constrained dynamic environment. The proposed method first constructs spatio-temporal driving space based on directed acyclic graph and efficiently searches a spatio-temporal trajectory using the improved A* algorithm. Then taking the search result as reference, locally convex feasible driving area is designed and model predictive control is applied to further optimize the trajectory with a comprehensive consideration of vehicle kinematics and moving obstacles. Results simulated in four different scenarios all demonstrated feasible trajectories without emergency stop or abrupt steering change, which is kinematic-smooth to follow. Moreover, the average planning time was 31 ms, which only took 59.05%, 18.87%, and 0.69%, respectively, of that consumed by other state-of-the-art trajectory planning methods, namely, maximum interaction defensive policy, sampling-based method with iterative optimizations, and Graph-search-based method with Dynamic Programming.