Using the non-standard three-point bending beam specimens of concrete, which have the span/ height ratio of 2.5, and the maximum load P_max and the correspoding crack mouth opening displacememt CMOD_c measured in the experiment, the precritical crack propagation length ∆a_c are evaluated by means of linear asymptotic superposition assumption. On this basis, the initiation fracture toughness Kⁱⁿⁱ_IC, unstable fracture toughness K^un_IC and the critical crack tip opening displacement CTOD_c for the non-standard three point bending beams with different initial crack lengths and different spcimen heights are determined utilizing fictitious crack model. The calculated results show that K^un_IC is independent of the initial crack length and the specimen height. Meanwhile, Kⁱⁿⁱ_IC is size-independent too, when a₀/h = 0.3〜0.5. This indicates that the double-K fracture parameter can be considered as a constant for concrete materials.