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A class of quasi-cubic Bezier curves (briefly QC-Bezier curves) with two shape parameters is presented in this paper. The QC-Bezier curves retain the main superiority of cubic Bezier curves. Unlike the existing techniques based on C-Bezier methods which can approximate the Bezier curves only from single side, the QC-Bezier curves can approximate the Bezier curve from the both sides. The curves include C-Bezier curves with α = π/2 as special case, and the change range of the curves is wider than that of C-Bezier curves. The shapes of the curves can be adjusted totally or locally. With the shape parameters and control points chosen properly, the introduced curves can represent some transcendental curves exactly.