  We construct a new cosmological holographic dark energy scenario based on
Loop Quantum Gravity inspired entropy, instead of the standard
Bekenstein-Hawking one. The former is an extended black-hole entropy that
arises from non-extensive statistics and quantum geometry and is quantified by
a new dimensionless parameter $q$, which possesses standard holographic dark
energy as a particular sub-case. In the future event horizon as the Infrared
cutoff, we provide a simple differential equation for the dark energy density
parameter, as well as an analytical expressions for the corresponding
equation-of-state and deceleration parameters. We show that the scenario at
hand can describe successfully the usual thermal history of the Universe, with
the sequence of matter and dark-energy epochs, while the transition to
acceleration takes place at $z\approx 0.6$. Additionally, according to the
value of the new entropic parameter $q$, the dark energy equation-of-state
parameter can have a rich behavior, and it can be quintessence-like,
phantom-like, or experience the phantom-divide crossing.
