Hydraulic concrete constructions are prone to cracking, which compromises the structure’s integrity and safety. To repair the cracks and reinforce the structure, effective measures must be implemented. A three-point bending concrete beam with precast cracks was taken as the research object to investigate the mechanical property and failure mode of the beam before and after it was repaired by high-strength epoxy mortar. Meanwhile a laboratory mechanical experiment was conducted to verify the accuracy of the material parameters and model settings. The bonding effect between the crack and the epoxy mortar interface was simulated using zero-thickness cohesive elements. The findings reveal that the bearing capacity of the concrete beam restored with high-strength epoxy mortar performed even better than that of the concrete beam without cracks. With the increase of the crack height ratio of the epoxy mortar, the ultimate bearing capacity of the concrete beam increased first and then stabilized. After achieving its final ultimate bearing capacity, the repaired concrete beam’s strength rapidly deteriorated. Finally, a calculation formula for quantifying the increment of the ultimate bearing capacity of concrete beams after repair with various crack height ratios was proposed, which can be used to provide technical assistance for the repair of concrete structures.