Taking into account the initial damage and the accumulation of damage of concrete, Mazars damage model was modified. Based on the modified Mazars damage model, combined with finite element software ANSYS, the fracture failure process of the three-point bending notched beam of concrete was simulated. The initiation load P ini and maximum load P max of the three-point bending beam were determined with the damage criterion, and the full relation curve of the load P versus the loading point displacement Δ of the fracture failure process of the three-point bending beam was obtained. The results show that the method of numerical simulation of concrete fracture failure process is feasible, and based on the initiation load of the crack determined by numerical simulation, the initiation toughness of the beam can be easily calculated, and the problem of calculation of the initiation toughness caused by the initiation load can not be accurately determined in the actual experiment is resolved.