  Employing the modified entropy-area relation suggested by Tsallis and Cirto
\cite{non3}, and the holographic hypothesis, a new holographic dark energy
(HDE) model is proposed. Considering a flat Friedmann-Robertson-Walker (FRW)
universe in which there is no interaction between the cosmos sectors, the
cosmic implications of the proposed HDE are investigated. Interestingly enough,
we find that the identification of IR-cutoff with the Hubble radius, can lead
to the late time accelerated Universe even in the absence of interaction
between two dark sectors of the Universe. This is in contrast to the standard
HDE model with Hubble cutoff, which does not imply the accelerated expansion,
unless the interaction is taken into account.
