Unlike a typical small-sized robot navigating in a free space, an autonomous vehicle has to travel in a designated road which has lanes to follow and traffic rules to obey. High-Definition (HD) maps, which include road markings, traffic signs, and traffic lights with high location accuracy, can help an autonomous vehicle avoid the need to detect such challenging road surroundings. With space constraints and a pre-built HD map, a new type of path planning algorithm can be conceived as a substitute for conventional grid-based path planning algorithms, which require substantial planning time to cover large-scale free space. In this paper, we propose an obstacle-avoiding, cost-based planning algorithm in a continuous space that aims to pursue a globally-planned path with the help of HD map information. Experimentally, the proposed algorithm is shown to outperform other state-of-the-art path planning algorithms in terms of computation complexity in a typical urban road setting, thereby achieving real-time performance and safe avoidance of obstacles