In this paper, we consider path planning for a car-like vehicle. Previous solutions to this problem computed paths made up of circular arcs connected by tangential line segments. Such paths have a non continuous curvature profile. Accordingly a vehicle following such a path has to stop at each curvature discontinuity in order to reorient its front wheels. To remove this limitation, we add a continuous-curvature constraint to the problem at hand. In addition, we introduce a constraint on the curvature derivative, so as to reflect the fact that a car-like vehicle can only reorient its front wheels with a finite velocity.We propose an efficient solution to the problem at hand that relies upon the definition of a set of paths with continuous curvature and maximum curvature derivative. These paths contain at most eight pieces, each piece being either a line segment, a circular arc of maximum curvature, or a clothoid arc. They are called SCC-paths (for Simple Continuous Curvature paths). They are used to design a local path planner, i.e. a non-complete collision-free path planner, which in turn is embedded in a global path planning scheme. The result is the first path planner for a car-like vehicle that generates collision-free paths with continuous curvature and maximum curvature derivative. Experimental results are presented.