An efficient and analytical continuous-curvature path-smoothing algorithm, which fits an ordered sequence of waypoints generated by an obstacle-avoidance path planner, is proposed. The algorithm is based upon parametric cubic Bézier curves; thus, it is inherently closed-form in its expression, and the algorithm only requires the maximum curvature to be defined. The algorithm is, thus, computational efficient and easy to implement. Results show the effectiveness of the analytical algorithm in generating a continuous-curvature path, which satisfies an upper bound-curvature constraint, and that the path generated requires less control effort to track and minimizes control-input variability.