A new geometric model of quartic generalized Bézier surfaces with multiple shape parameters was constructed by using a class of quartic generalized Bernstein basis functions. The proposed quartic generalized Bézier surfaces inherit the outstanding properties of conventional Bézier Surfaces, have a good performance on adjusting their shapes by changing shape control parameters, and have quartic Bézier surfaces as their special cases. Some basic properties of the surfaces were analyzed, and the constructions of some special surfaces degenerated from the generalized surfaces were discussed. With the aim to tackle the problem that the engineering complex surfaces can not be constructed by a single surface, the continuity conditions of quartic generalized Bézier surfaces with shape parameter were investigated. Based on the analysis of the basis functions, the conditions of G1 and G2 continuity between two adjacent quartic generalized Bézier surfaces and the detail process to blend the two surfaces were proposed. In addition, some applications of the quartic generalized Bézier surfaces in geometric modeling were discussed. The modeling examples show that the proposed method is effective and easy to implement and has extensive applications in constructing engineering complex surface.