Vehicle trajectory planning is a key component for an autonomous driving system. A practical system not only requires the component to compute a feasible trajectory, but also a comfortable one given certain comfort metrics. Nevertheless, computation efficiency is critical for the system to be deployed as a commercial product. In this paper, we present a novel trajectory planning algorithm based on nonlinear optimization. The algorithm computes a kinematically feasible and comfort-optimal trajectory that achieves collision avoidance with static obstacles. Furthermore, the algorithm is time efficient. It generates an 6-second trajectory within 10 milliseconds on an Intel i7 machine or 20 milliseconds on an Nvidia Drive Orin platform.