As for curvature continuity curves, they are usually constructed by means of rational cubic curves. A method for interpolating global curvature continuity curves with conic segments is presented in this paper. Firstly, the curvature continuity conditions between two adjacent rational quadratic curve segments are derived. Secondly, an optimal algorithm is presented for solving out the tangent lines at every points of a closed point set in a plane. Finally, several examples are given out to illustrate the effectiveness of this method.