  Recently, the R\'{e}nyi and Tsallis generalized entropies have extensively
been used in order to study various cosmological and gravitational setups.
Here, using a special type of generalized entropy, a generalization of both the
R\'{e}nyi and Tsallis entropy, together with holographic principle, we build a
new model for holographic dark energy. Thereinafter, considering a flat FRW
universe, filled by a pressureless component and the new obtained dark energy
model, the evolution of cosmos has been investigated showing satisfactory
results and behavior. In our model, the Hubble horizon plays the role of IR
cutoff, and there is no mutual interaction between the cosmos components. Our
results indicate that the generalized entropy formalism may open a new window
to become more familiar with the nature of spacetime and its properties.
