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In this study, the element-free Galerkin (EFG) method is extended to include nonlinear behavior of cohesive cracks in 2D domains. A cohesive curved crack is modeled by using several straight-line interface elements connected to form the crack. The constitutive law of cohesive cracks is considered through the use of these interface elements. The stiffness equation of the domain is constructed by directly including, in the weak form of the global system equation, a term related to the energy dissipation along the interface elements. The constitutive law of cohesive cracks can then be considered directly and efficiently by using this energy term. The validity and efficiency of the proposed method are discussed by using problems found in the literature. The proposed method is found to be an efficient method for simulating propagation of cohesive cracks.