In this paper, we study spatially homogeneous and anisotropic Bianchi type-V and IX universes filled with interacting dark matter and holographic dark energy. We obtained the solution of the field equations by using the variable deceleration parameter in the form R(t) = t(delta)e(gamma t). The cosmological parameters of the models like deceleration and equation of state are obtained. We observe that the deceleration parameter tends to -1 which shows an accelerated universe, and the equation of state tends to -1 which belongs to Lambda CDM model. Moreover, we establish the correspondence between holographic dark energy model and quintessence scalar field.