This study developed a novel approach to measure the intrinsic fracture toughness of full-depth fiber reinforced concrete (FRC) and functionally graded concrete (FGC) beams. Three concrete mixes were prepared to cast FGC beams, namely normal strength concrete to be cast in the middle layer of the FGC beams, FRC with 1% hooked-end steel fiber, to be cast in the bottom layer (tensile layer), and high strength concrete (HSC) to be cast in the top layer (compressive layer). Ninety-six un-cracked and matrix-cracked (crack length to depth ratio equals 1/3) FRC and FGC beams were cast and tested under 3 PB. These beams included three span-length to depth (L/d) ratios, 4, 5, and 6. The fracture toughness was measured based on the present proposed method and Hillerborg's concept, i.e., work of fracture method (WFM). The applicability of these methods was judged based on the maximum size of the non-damaged defect (dmax) concept. The results showed that FGC beams exhibited better efficiency compared to FRC. The suggested matrix-cracked created in the concrete beams represented actual field crack for FRC specimens. It showed its effectiveness in indicating the closure moment effect of short fibers in matrix-cracked specimens. According to the dmax concept, i.e., the ratio of dmax to nominal maximum aggregate size (NMAZ), the intrinsic fracture toughness calculated by the proposed method can be considered a reasonable candidate to predict the fracture behavior of FRC and FGC beams. On contract, WFM showed that the ratio of dmax/NMAZ is very far from unity.