Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions |x 1|α 1 . . . |xd |αd on the unit sphere S d-1 in ℝd . The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.