  The existence of the QCD critical point at non-zero baryon density is not
only of great interest for experimental physics but also a challenge for the
theory. Any hint of the existence of the first order phase transition and,
particularly, its critical point will be valuable towards a full understanding
of the QCD phase diagram. We use lattice simulation based on the canonical
ensemble method to explore the finite baryon density and finite temperature
region and look for the QCD critical point. As a benchmark, we run simulations
for the four degenerate flavor QCD where we observe a clear signal of the
expected first order phase transition. In the two flavor case, we do not see
any signal for temperatures as low as $0.83 \rm{T_c}$. Although our real world
contains two light quarks and one heavier quark, three degenerate flavor case
shares a lot of similar phase structures as the QCD. We scan the phase diagram
using clover fermions with $m_\pi \approx 700{MeV}$ on $6^3\times4$ lattices.
The baryon chemical potential is measured as we increase the baryon number and
we see the characteristic "S-shape" that signals the first order phase
transition. We determine the phase boundaries by Maxwell construction and
report our preliminary results for the location of critical point for the
present lattice.
