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 and
zero chemical potential to the case of finite chemical potential and zero
temperature, and calculate the equation of state (EOS) for (2+1) flavor Quantum
Chromodynamics (QCD) at zero temperature and high density. We first calculate
the partition function at finite temperature and chemical potential, then go to
the 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 EOS
to calculate the quark-number density, the energy density, the quark-number
susceptibility and the speed of sound at zero temperature and finite chemical
potential and compare our results with the corresponding ones in the existing
literature
