A method is presented for constructing surfaces on irregular meshes. The basic idea is to extend the B-spline method to irregular meshes through the decomposition and classification of uniform bi-cubic B-spline basis function. Given a quad mesh of control points, a basis function is constructed for each control point. Then the surface is defined by the weighted combination of all the control points using their associated basis functions. This surface is a piecewise bi-cubic rational parametric polynomial surface. It is an extension to uniform B-spline surfaces in the sense that its definition is an analogy of the B-spline surface, and it produces a uniform bi-cubic B-spline surface if the control mesh is a regular quad mesh. Examples are also included to show that the new method can be used to construct surface on irregular meshes effectively.