  We study the phase structure of QCD at finite temperature and density by
numerical simulations on a lattice. The most important point for the numerical
study at finite density is treatment of the sign problem. We propose a method
to avoid the sign problem, which is based on a cumulant expansion of the
complex phase in the density of state method combined with the reweighting
method. Using the method, we study the critical point terminating a first order
phase transition line in lattice QCD at high temperature and density.
