  The QCD thermodynamics on the lattice provides fundamental theoretical
grounds to analyze the various experimental data in relativistic heavy ion
collisions. So far, most of the numerical simulations on the lattice have been
performed by using the staggered-type fermion actions. Therefore it is
important to carry out studies using different fermion formulations to test the
uncertainties of the lattice QCD results. For this purpose, we perform
systematic simulations of two-flavor QCD with an improved Wilson quark action
to investigate the equation of state. We report the current status of our
project and show the preliminary results of the Taylor expansion coefficients
of the thermodynamic grand partition function in terms of chemical potential.
