  The cluster abundance and its redshift evolution are known to be a powerful
tool to constrain the amplitude of mass fluctuations \sigma_8 and the mass
density parameter \Omega_m0. We study the impact of the finite decay rate of
cold dark matter particles on the cluster abundances. On the basis of spherical
model in decaying cold dark matter universe, we calculate the mass function of
clusters and compare it with observed cluster abundance. We find the decay of
cold dark matter particles significantly changes the evolution of the cluster
abundance. In particular, we point out that the lifetime of dark matter
particles comparable to the age of the universe lowers the ratio of the local
cluster abundance to the high-redshift cluster abundance and can account for
the observed evolution of the cluster abundance quite well. The strong
dependence of the cluster abundance on the decay rate of dark matter suggests
that distant cluster surveys may offer clues to the nature of dark matter.
