Abstract: To tackle the problem that the engineering complex curves or surfaces can not be constructed by using a single curve or surface, the continuity condition of quartic quasiBézier(quartic qBézier) curves and surfaces with shape parameters was studied. Based on the analysis of the basis functions and terminal properties, the necessary and sufficient conditions of G1 and G2 continuity, and C1 and C2 continuity between two adjacent quartic qBézier curves were proposed. In order to overcome the shortcomings that the circular arc and ellipse can not be accurately represented by quartic qBézier curves, the continuity condition between quartic qBézier curves and CBézier curves was also presented. In addition, the geometric model of the quartic qBézier surfaces was constructed and the condition of G1 continuity between two adjacent quartic qBézier surfaces in u and v directions was derived and simplified by choosing the control parameters properly. The modeling examples illustrated that the continuity condition of the quartic qBézier curves and surfaces could be widely applied to the complex curves and surfaces modeling system.