The fracture behavior of a graphene sheet containing a center crack was characterized based on the viewpoints of atomistic simulation and continuum mechanics. Two failure modes, i.e., opening mode (Mode I) and sliding mode (Mode II), were considered by applying remote tensile and shear loading, respectively on the graphene sheet. In the atomistic simulation, the equilibrium configurations of the cracked graphene subjected to applied loadings, before and after the crack extension of 2?a , were determined through molecular dynamics (MD) simulation, from which the potential energy variation and the strain energy release rate of the discrete graphene sheet due to crack extension was then calculated accordingly. It is noted that because of the discrete attribute, there is no stress singularity near the crack tip and thus, the concept of stress intensity factor which is generally employed in the continuum mechanics may not be suitable for modeling the crack behavior in the atomistic structures. For the comparison purpose, the continuum finite element model with the same geometric parameters and material properties as the atomistic graphene sheet was constructed and the corresponding strain energy release rate was calculated from the crack closure method. Results indicated that the strain energy release rates obtained from continuum model exhibit good agreement with those derived from discrete atomistic model. Therefore, it is suggested that the concept of strain energy release rate is an appropriate parameter which can be applicable to both the atomistic model and the continuum model for describing the fracture of covalently bonded graphene sheet.