Summary: The \(Z\)-eigenvalues of tensors play an important role in many scientific fields such as medical resonance imaging and positive definiteness of even-order multivariate forms. A new inclusion theorem for the \(Z\)-eigenvalue of tensors is given. As applications, a new upper bound for the \(Z\)-spectral radius of nonnegative tensors is obtained. Numerical experiments are given to show the efficiency of our new results.