Using Galerkin Finite Volume method, a 2D adaptive algorithm is developed for crack propagation simulation of concrete structures under mixed mode loading. The matrix free Finite Volume formulation is applied to implement a crack propagation model in a fully automatic adaptive mesh refinement framework for unstructured meshes. Cohesive cracks are implemented using nonlinear interface elements with bilinear softening constitutive equation. On contrary to existing cohesive crack models where the Newton-Raphson techniques are required to simulate the nonlinear behavior in the fracture process zone, the need for such a computational costly technique is relaxed. The matrix-free Finite Volume formulation method can provide better computational performance than the matrix-base methods. The introduced Method can also relax the problems of the standard Finite Element base methods with high aspect-ratio elements. The present Finite Volume model accurately predicts the crack propagation path and correctly evaluates the load-displacement curve while consumes low computational CPU time.