Discrete element method (DEM) has been proved to be a great tool to simulate and analyze the behavior of rock material, However, classic DEM using symmetrical particles bears the intrinsic limitation of severely overestimating the tensile strength of cohesive-frictional material and causing unrealistically low unconfined compressive strength (UCS) to tensile strength (T) ratio. This paper proposes a new contact model which properly considers the contribution of moments to the contact stresses and the condition at which the contact fails. The contact model has been implemented in the three-dimensional Particle Flow Code (PFC3D) and the detailed parametric study indicates that the moment contribution to the contact stresses is a major factor affecting the UCS/T ratio of PFC specimens. After decreasing the moment contribution parameter to be smaller than 0.5, a wide range of UCS/T ratios can be achieved by using different cohesion and tensile strength values. This new contact model has been used to simulate the behavior of Lac Du Bonnet (LDB) granite and Carrara marble and satisfactory UCS/T ratios agreeing with the measured values are obtained.