We consider the power law and the entropy corrected holographic dark energy (HDE) models with Hubble horizon in the dynamical Chern-Simons modified gravity. We explore various cosmological parameters and planes in this framework. The Hubble parameter lies within the consistent range at the present and later epoch for both entropy corrected models. The deceleration parameter explains the accelerated expansion of the universe. The equation of state (EoS) parameter corresponds to quintessence and cold dark matter (ACDM) limit. The omega(A)-omega'(A) approaches to.CDM limit and freezing region in both entropy corrected models. The statefinder parameters are consistent with ACDM limit and dark energy (DE) models. The generalized second law of thermodynamics remain valid in all cases of interacting parameter. It is interesting to mention here that our results of Hubble, EoS parameter and omega(A)-omega'(A) plane show consistency with the present observations like Planck, WP, BAO, H-0, SNLS and nine-year WMAP.