We formulate an explicit form of degree-ordered system of bivariate generalized Chebyshev Koornwinder’s type polynomials Un,r,d(γ,Μ,Ν)(u,v,w), γ > −1 in Bezer form over a triangular domain T. These polynomials form an orthogonal system with respect to the generalized measure 2π1-x2+Μδ−1+Nδ1 where M, N ≥ 0 and δx is a singular Dirac measure. Then, we study cu-bature formulas to approximate double integrals for bivariate generalized Chebyshev Koornwinder’s type polynomials, Un,r,d(γ,Μ,Ν)(U) over T.