A rapid path-planning algorithm that generates drivable paths for an autonomous vehicle operating in structural road is proposed in this paper. Cubic B-spline curve is adopted to generating smooth path for continuous curvature and, more, parametric basic points of the spline is adjusted to controlling the curvature extremum for kinematic constraints on vehicle. Other than previous approaches such as inverse kinematics, model-based prediction postprocess approach or closed-loop forward simulation, using the kinematics model in each iteration of path for smoothing and controlling curvature leading to time consumption increasing, our method characterized the vehicle curvature constraint by the minimum length of segment line, which synchronously realized constraint and smooth for generating path. And Differ from the path of robot escaping from a maze, the intelligent vehicle traveling on road in structured environments needs to meet the traffic rules. Therefore, the path could be simplified and segmented to four basic parts: go straight, lane change/merge, turn and U-turn. By given reasonable start and terminal, all the basic segments could be generated via parameterized cubic B-spline curve and a complete executable path would be connected by the four parts. In order to increase the comfortable capability by reducing extreme points of curvature and control the curvature extremum by steerable, an improvement program is employed, which assorts secondary spiral and arc to replacing the B-spline curve in generating segment of turn and U-turn. The simulation and real vehicle experimental results illustrate that the method in this paper is fast in generating drivable smooth path.