In this paper, we propose a mixed generalized Laguerre-Legendre pseudospectral method for non-isotropic heat transfer with inhomogeneous boundary conditions on an infinite strip. Some properties about the mixed generalized Laguerre-Legendre approximation are established. By reformulating the equation with suitable functional transform defined on an infinite strip, a mixed Laguerre-Legendre pseu-dospectral scheme is constructed. Its convergence is proved. Numerical results are presented to demonstrate the efficiency of this new approach and to validate our theoretical analysis.