Abstract: This paper proposes the concept of blending time-dependent varying surfaces, and develops a new method to create a controllable C1 continuous blending surface between primary parametric surfaces whose position and shape change with time. We treat it as a boundary-valued problem defined by the mathematical model of a vectored dynamic fourth-order partial differential equation subjected to time-dependent C1 continuous blending boundary constraints. High performance blending surface generation is achieved through the development of an approximate analytical solution of the mathematical model. We investigate the accuracy and efficiency of the solution, study the effective shape control of the blending surfaces, and apply the obtained solution to tackle surface blending problems. The applications demonstrate that our proposed approach is very effective and efficient in dealing with controllable C1 continuous surface blending between time-dependent varying parametric surfaces.