From typical stress-axial strain curve and stress-volume strain curve of a concrete under uniaxial compression, the initiation and localization of microcracks within the interior of the specimen can be identified. The occurrence of random microcrack indicates the end of the linear elasticity, and the localization of microcrack implies formation of major crack, which triggers the onset of unstable crack propagation. The interval between initiation and localization of microcracks is characterized by a stable microcrack growth. Based on fracture behavior observed from a uniaxial compressive test of a concrete cylinder, a model has been developed to extract fundamental fracture properties of a concrete, i.e. the equivalent fracture toughness and the size of fracture process zone. The introduction of cracking Poisson's ratio accounts for tensile failure characteristics of concrete even under uniaxal compression. To justify the validity of the model proposed, tests on three-point bending have been performed to obtain the fracture toughness in accordance with two parameter fracture model and double-K fracture model. Surprisingly, it yields favorably comparable results and provides an encouraging alternative approach to determine fracture properties for concretes.