A set of new Bell inequalities with universality can clearly describe the relationship between the nonlocality and three-body entanglement of three-qbit generalized Greenberger-Horne-Zeilinger(GGHZ) states. Three-photon GGHZ entangled states are prepared by using high-energy femtosecond laser parametric conversion. The state fidelity calculated by quantum state chromatography is 84%. A novel Bell operator and Bell inequality are measured based on the high fidelity three-photon GGHZ state. The results are in agreement with the theory, and the theoretical results proposed by Das are verified by experiments. Experimental results show that the violation to the local realism of the new Bell inequality increases monotonously with the increasing of GGHZ states entanglement degree. The nonlocality of GGHZ states is directly related to the degree of three-body entanglement.