  In this paper we consider holographic dark energy model with corrected
holographic energy density and show that this model may be equivalent to the
modified Chaplygin gas model. Then we obtain relation between entropy corrected
holographic dark energy model and scalar field models. We do these works by
using choices of IR cut-off length proportional to the Hubble radius, the event
horizon radius, the Ricci length, and the Granda-Oliveros length.
