In this paper, we theoretically study the relation between concurrence and nonlocality depicted by Bell-type inequality violation of quantum mechanics prediction versus local realism prediction for the GHZ (Greenberger -Horne-Zeilinger) class states. Analytical expressions of concurrence, violations of the Mermin inequality and the Svetlichny inequality are obtained. Through numerical calculations, the relationship between entanglement and nonlocality of GHZ-class states is discussed. Our results show that the concurrence is consistent with the degree of nonlocality described by violations of the two Bell-type inequalities of GHZ-class states. The Bell operator and its parameters can obviously reveal the nonlocal features of quantum states.