Based on the extended finite element method (XFEM), the fracture failure process of concrete three-point bending beams with different widths was simulated, and the load-crack mouth displacement curve (P-CMOD) was obtained. The fracture process of three-point bending beam with different width, crack height ratio and span height ratio was simulated, and the stress intensity factor under different width, crack height ratio and span ratio was obtained by using the double K fracture criterion. The influence of these three parameters on the stress intensity factor was studied. The results show that the initiation fracture toughness K_Icⁱⁿⁱ and unstable fracture toughness K_Ic^un of three-point bending beam with span-depth ratio and crack-depth ratio equal to 0.4 basically remain unchanged when the beam width changes from 100 mm to 250 mm. When the beam width was constant, the span-depth ratio was 4 and the crack-depth ratio increases from 0.2 to 0.5, the initiation fracture toughness K_Icⁱⁿⁱ and the unstable fracture toughness K_Ic^un increase first and then decrease. When the beam width was constant, the crack height ratio was equal to 0.4, and the span height ratio increases from 2.5 to 3.5, the initial fracture toughness K_Icⁱⁿⁱ remains unchanged, and the unstable fracture toughness K_Ic^un will gradually increase but the amplitude was small. When the span-to-height ratio was constant, the crack-to-height ratio was equal to 0.4, and the beam width changes in the range of 100~250 mm, the initial fracture toughness K_Icⁱⁿⁱ and the unstable fracture toughness K_Ic^un all increase first and then decrease, indicating that K_Icⁱⁿⁱ and K_Ic^un with small span-to-height ratio have a certain size effect in the beam width direction.