Abstract: Zero-difference balanced(ZDB) functions were introduced by Ding in connection with construction of optimal constant composition codes and optimal and perfect difference systems of sets. Based on such functions, people have been constructed optimal constant weight codes and optimal frequency hopping sequences. Here the zero-difference balanced function was generalized to the generalized zero-difference balanced (G-ZDB) function, and based on properties of p-cyclotomic cosets, several new classes of generalized zero-difference balanced functions were constructed.