With a theoretical basis more rigorous than the limit equilibrium method, the upper-bound limit finite element method can be used to determine not only the safety factor of slope but also the critical slip surface so that it will have a broad prospect of application. To remove the limitation that the traditional upper-bound limit finite element method cannot address the effect of heterogeneity, a new Mohr-Coulomb yield surface linearization method is proposed herein, based on the linearized spatial discretization. Within this context, the linearized constraint equations for plastic flow are developed, which enriches the upper-bound limit method based on linear programming and lays a solid foundation for the application of linear programming technics to the upper-bound limit analysis. Two examples are analyzed, showing that the proposed method stably yields a convergent solution from above the upper-bound solution. In analyzing the stability of a slope, if the strength anisotropy is ignored, the factor of safety is overestimated, resulting in a larger factor of safety of the slope.