In this work, we apply the multiscale cohesive method (Zeng and Li, 2010, “A Multiscale Cohesive Zone Model and Simulations of Fracture,” Comput. Methods Appl. Mech. Eng., 199, pp. 547–556) to simulate fracture and crack propagations in polycrystalline solids. The multiscale cohesive method uses fundamental principles of colloidal physics and micromechanics homogenization techniques to link the atomistic binding potential with the mesoscale material properties of the cohesive zone and hence, the method can provide an effective means to describe heterogeneous material properties at a small scale by taking into account the effect of inhomogeneities such as grain boundaries, bimaterial interfaces, slip lines, and inclusions. In particular, the depletion potential of the cohesive interface is made consistent with the atomistic potential inside the bulk material and it provides microstructure-based interface potentials in both normal and tangential directions with respect to finite element boundary separations. Voronoi tessellations have been utilized to generate different randomly shaped microstructure in studying the effect of polycrystalline grain morphology. Numerical simulations on crack propagation for various cohesive strengths are presented and it demonstrates the ability to capture the transition from the intergranular fracture to the transgranular fracture. A convergence test is conducted to study the possible size-effect of the method. Finally, a high-speed impact example is reported. The example demonstrates the advantages of multiscale cohesive method in simulating the spall fracture under high-speed impact loads.