Abstract: In order to simplify the problem of smoothing connection of triangular Bézier patches around a common vertex,a system of equations about the interpolating data is obtained according to the geometric feature of smoothing connection and consistence conditions.According to the conditions that the system has solutions,the methods for constructing polynomial surfaces with a common vertex and with G¹,G² and Gaussian curvature continuity are presented respectively.Then we get the methods for smoothing connection of triangular Bézier patches with a common vertex by transforming polynomial surfaces to triangular Bézier patches.The resulting polynomial surfaces have lower degree and can be adjusted easily,their degrees are 3,5 and 4 for G¹,G² and Gaussian curvature continuity respectively.The examples show that the methods are efficient and flexible for local shape adjustment.