  We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time
with two fluids as the content of the Universe: matter and holographic dark
energy in the framework of general relativity. To get the exact solutions of
Einstein's field equations, we choose the scale factor as a hyperbolic
function, specifically, $a\left( t\right) =\sinh ^{\frac{1}{n}}\left( \gamma
t\right) $, where $\gamma $ and $n>0$ are arbitrary constants, which gives us a
time-dependent deceleration parameter. Then we study our cosmological model
under the conditions of the parameters as: $\gamma $ fixed and $n>1$. Our
cosmological solutions led to an early deceleration phase followed by the
current observed acceleration phase. Further, the anisotropic parameter and
some other physical parameters are discussed. We conclude that our cosmological
model is consistent with the results of recent astronomical observations.
