To meet the strict requirements for the control points made by the G2 continuity conditions of the Bézier curve and many existing extended Bézier curves with shape parameter, a G2 continuous composite curve representation method was proposed. The method could synthesize the advantages of the Bézier method and B-spline method, and its basis function had explicit expression. It was of the automatic smoothness as that of the B-spline method, easily possessing the end-point geometric characteristic of the Bézier curve. To this end, a set of basis function with six parameters was constructed. On this basis, a curve segment based on four control points was constructed according to the definition mode of the cubic Bézier curve. According to the -continuity conditions between the curve segments, a kind of composite curve on four-point piecewise scheme was constructed according to the definition mode of the cubic B-spline curve. The basis function was of total positivity, and contained the cubic Bernstein basis functions and the cubic B-spline basis functions that were determined by the node vector with the repetition degree of all internal nodes being one. The curve segment had the feature of convexity-preserving, endpoint position, and adjustable shape, and contained the cubic Bézier curve and the cubic B-spline curve segment as special cases. The definition of the composite curve could automatically ensure its G2 continuity at each junction. The composite curve could have end-point interpolation and end-edge tangency by setting some of its parameters as specific values. At this point, the composite curve still contained independent parameters used to adjust its internal shape. As long as the parameters of the composite curve were selected according to certain rules, the C2 continuous cubic B-spline curve could be reconstructed.