  Using the nucleon coalescence model, which can naturally take into account
the correlations in the nucleon density distribution, we study the effects of
QCD critical point on light nuclei production in relativistic heavy-ion
collisions. We find that the yield ratio $N_tN_p/N_d^2$ of proton ($p$),
deuteron ($d$) and triton ($t$) increases monotonically with the nucleon
density correlation length, which is expected to increase significantly near
the critical point in the QCD phase diagram. Our study thus demonstrates that
the yield ratio $N_tN_p/N_d^2$ can be used as a sensitive probe of the QCD
critical phenomenon. We further discuss the relation between the QCD phase
transitions in heavy-ion collisions and the possible non-monotonic behavior of
\pdt~in its collision energy dependence.
