Abstract: A class of bivariate polynomial weight function of degree (n+1) with a parameter is presented in this paper.They are an extension of bivariate n-degree Bernstein basis functions.Properties of this new basis are analyzed and the (n+1)-degree triangular Bézier surface with a shape parameter is defined based on them.The surface not only inherits the most properties of n-degree triangular Bézier surface,but also can adjust itself shape through changing the value of parameter.And it is endowed the property of geometry.The larger is the parameter,the more approaches the surface to the control net.When parameter vanishes,the surface degenerates to n-degree triangular Bézier surface.