  Clusters of galaxies in most previous catalogs have redshifts z<0.3. Using
the photometric redshifts of galaxies from the Sloan Digital Sky Survey Data
Release 6 (SDSS DR6), we identify 39,668 clusters in the redshift range 0.05< z
<0.6 with more than eight luminous (M_r<-21) member galaxies. Cluster redshifts
are estimated accurately with an uncertainty less than 0.022. The contamination
rate of member galaxies is found to be roughly 20%, and the completeness of
member galaxy detection reaches to ~90%. Monte Carlo simulations show that the
cluster detection rate is more than 90% for massive (M_{200}>2\times10^{14}
M_{\odot}) clusters of z<0.42. The false detection rate is ~5%. We obtain the
richness, the summed luminosity, and the gross galaxy number within the
determined radius for identified clusters. They are tightly related to the
X-ray luminosity and temperature of clusters. Cluster mass is related to the
richness and summed luminosity with M_{200}\propto R^{1.90\pm0.04} and
M_{200}\propto L_r^{1.64\pm0.03}, respectively. In addition, 685 new candidates
of X-ray clusters are found by cross-identification of our clusters with the
source list of the ROSAT X-ray survey.
