  Recent studies of structures of galaxies and clusters imply that dark matter
might be unstable and decay with lifetime $\Gamma^{-1}$ about the age of
universe. We study the effects of the decay of cold dark matter on the
Sunyaev-Zel'dovich (SZ) power spectrum. We analytically calculate the SZ power
spectrum taking finite lifetime of cold dark matter into account. We find the
finite lifetime of dark matter decreases the power at large scale ($l < 4000$)
and increases at small scale ($l > 4000$). This is in marked contrast with the
dependence of other cosmological parameters such as the amplitude of mass
fluctuations $\sigma_{8}$ and the cosmological constant $\Omega_{\lambda}$
(under the assumption of a flat universe) which mainly change the normalization
of the angular power spectrum. This difference allows one to determine the
lifetime and other cosmological parameters rather separately. We also
investigate sensitivity of a future SZ survey to the cosmological parameters
including the life time, assuming a fiducial model $\Gamma^{-1} = 10 h^{-1}
{\rm Gyr}$, $\sigma_{8} = 1.0$, and $\Omega_{\lambda} = 0.7$. We show that
future SZ surveys such as ACT, AMIBA, and BOLOCAM can determine the lifetime
within factor of two even if $\sigma_{8}$ and $\Omega_{\lambda}$ are
marginalized.
