Purpose of this paper is to study generalized quantum chromodynamics ghost DARK ENERGY (GDE) in the frame work of Horava–Lifshitz cosmology. Considering interacting and non-interacting scenario of GDE with DARK matter in a spatially non-flat universe, we investigate the cosmological implications of this model in detail. We obtain equation of state parameter, deceleration parameter and the evolution of DARK ENERGY density to explain the expansion of the universe. Also, we show that the results we calculate have a good compatibility with previous work and restore it in limiting case. Further, we investigate validity of generalized second law of thermodynamics in this scenario. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of DARK ENERGY for law redshifts.