A modifiable quasi cubic curve based on functions 1, sinu, cosu, sin2u is presented in this paper. The curve is controlled by four points, and it has a lot of similar characteristics to the cubic Bézie curve, and its shape can be adjusted by a parameter, which makes the curve have more powerful expression ability. For designing free curves, the continuity condition of twopiece curves is discussed. As a result, the continuity of the curve is better than the cubic Bézier curve, twopiece curves can be C3 continuous when choosing a proper shape parameter, and the continuity condition of the curve is simpler than the cubic Bézier curve. In addition, the curve can represent elliptic curves, parabola and other conical curves without using a rational form, which is helpful for practical applications.