  Thermodynamics-Gravity conjecture implies that there is a deep connection
between the gravitational field equations and the first law of thermodynamics.
Therefore, any modification to the entropy expression, directly modifies the
field equations. By considering the modified Barrow entropy associated with the
apparent horizon, the Friedmann equations get modified as well. In this paper,
we reconsider the holographic dark energy (HDE) model when the entropy is in
the form of Barrow entropy. This modification to the entropy not only changes
the energy density of HDE, but also modifies the Friedmann equations.
Therefore, one should take into account the modified HDE in the context of
modified Friedmann equations. We study the Hubble horizon and the future event
horizon as IR cutoffs, and investigate the cosmological consequences of this
model. We also extend our study to the case where dark matter (DM) and dark
energy (DE) interact with each other. We observe that Barrow exponent $\delta$
significantly affects the cosmological behavior of HDE, and in particular the
equation of state (EoS) parameter can cross the phantom line $(w_{de}<-1)$.
Also adding $\delta$ remarkably affects the deceleration parameter, and shifts
the time of universe phase transition.
