In this paper, we introduce a quantity which is called exponential entropy of ‘type (α, β)’ and discuss its some major properties corresponding to exponential entropy of concave function. Further, we define an exponential directed-divergence convex function of ‘type (α, β)’. From this directed-divergence measure a new exponential information measures have also been derived when one of the probability distribution is uniform. Tsallis’ -Havrda -Charvat, Takuya Yamano, Sharma and Mittal relative entropies are the particlular cases of the proposed measure.