  Using the photometric redshifts of galaxies from the Sloan Digital Sky Survey
III (SDSS-III), we identify 132,684 clusters in the redshift range of
0.05<z<0.8. Monte Carlo simulations show that the false detection rate is less
than 6% for the whole sample. The completeness is more than 95% for clusters
with a mass of M_{200}>1.0*10^{14} M_{\odot} in the redshift range of
0.05<z<0.42, while clusters of z>0.42 are less complete and have a biased
smaller richness than the real one due to incompleteness of member galaxies. We
compare our sample with other cluster samples, and find that more than 90% of
previously known rich clusters of 0.05<z<0.42 are matched with clusters in our
sample. Richer clusters tend to have more luminous brightest cluster galaxies
(BCGs). Correlating with X-ray and the Planck data, we show that the cluster
richness is closely related to the X-ray luminosity, temperature and
Sunyaev-Zel'dovich measurements. Comparison of the BCGs with the SDSS luminous
red galaxy (LRG) sample shows that 25% of LRGs are BCGs of our clusters and 36%
of LRGs are cluster member galaxies. In our cluster sample, 63% of BCGs of
r_{petro}<19.5 satisfy the SDSS LRG selection criteria.
