A series of numerical simulation of constant b cubic tests are conducted using discrete element method to study the strength characteristics of granular materials under different stress paths. The influences of intermediate principal stress and stress path on the peak strength of granular materials are analyzed in 3-dimensional stress state based on the simulation numerical results. The variation of peak friction angle and peak stress ratio is also studied. Contributions to strength of granular materials are analyzed based on the true stress concept and the development of fabric tensor. Research results show that the variations of peak deviatoric stress with Bishop parameter are different in different type cubic tests; however, the stress-strain curves normalized by the initial confining stress are identical. The slope of peak strength line independent of stress path is only related to parameter b; and the peak stress ratio qf /pf decreases with an increase of b. Simulation results are in agreement with laboratory observations. Meanwhile, stress-induced fabric anisotropy is developed with the increasing strain. The strength of granular materials is the joint action of friction of particles and anisotropic fabric induced by the applied stress. Theoretically, the location of failure point in fabric ratio-stress ratio coordinate system is only decided by the particle apparent friction angle. The deviation between numerical simulation and theoretical analysis is origin from the effect of interlocking and rolling friction between particles and this influence is related to both particle friction coefficient and stress state.