  We consider the holographic dark energy model with axial torsion which
satisfy the cosmological principle. Subsequently, by using the torsional
analogues of Friedmann equations for the new equation from Einstein-Cartan
gravity theory, we obtain the equation of state for dark energy in this model.
We find that the extended holographic dark energy from the particle horizon as
the infrared (IR) cut-off does not give the accelerating expansion of the
universe. Also, employing the future event horizon as IR cut-off still achieves
the accelerating expansion of the universe. In contrast, there is a possibility
that the Hubble radius as IR cut-off achieves to the accelerating expansion of
the universe in superluminal region for axial torsion. More precisely, the
current value of ratio for torsion to the matter density, $\gamma^{0}=0.5$
gives the equation of state of dark energy $\omega_{\Lambda}\cong-1$.
