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In this paper, we generalize the improved quasi-particle model proposed in J.Cao et al., [ Phys. Lett. B {\bf711}, 65 (2012)] from finite temperature andzero chemical potential to the case of finite chemical potential and zerotemperature, and calculate the equation of state (EOS) for (2+1) flavor QuantumChromodynamics (QCD) at zero temperature and high density. We first calculatethe partition function at finite temperature and chemical potential, then go tothe limit $T=0$ and obtain the equation of state (EOS) for cold and dense QCD,which is important for the study of neutron stars. Furthermore, we use this EOSto calculate the quark-number density, the energy density, the quark-numbersusceptibility and the speed of sound at zero temperature and finite chemicalpotential and compare our results with the corresponding ones in the existingliterature.

A thermodynamically consistent quasi-particle model without density-dependent infinity of the vacuum zero point energy