We provide a method to describe quantum nonlocality for (n)-qubit systems. By treating the correlation function as an (n)-index tensor, we derive a generalized Bell inequality. Taking generalized Greenberger-Horne-Zeilinger (GHZ) state for example, we calculate quantum prediction under a series of measurement settings involving various angle parameters. We reveal the exact relationship between quantum prediction and the angle parameters. We show that there exists a set of optimal measurement settings and find the corresponding maximal quantum prediction for (n)-qubit generalized GHZ states. As an example, we consider an interesting situation involving only two angle parameters. Finally, we obtain a criterion for the violation of the generalized Bell inequality.