In order to study as a whole a wide part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to theh-derivative, which generalizes the conventional Newton–Leibniz calculus. This new entropy,Sh,h′, is proved to describe the non-extensive systems and recover several types of well-known non-extensive entropic expressions, such as the Tsallis entropy, the Abe entropy, the Shafee entropy, the Kaniadakis entropy and even the classical Boltzmann–Gibbs one. As a generalized entropy, its corresponding properties are also analyzed.