Abstract: Statistical analysis for 109 X-ray selected quasars as well as 114 radio and optically selected quasars ds carried out in this paper. On the histograms of their redshift, optical luminosity and average optical X-ray spectral index, it is found that X-ray selected quasars are distributed at the low ends of plots of these parameters. On the plot of the monochromatic X-ray luminosity against the monochromatic optical luminosity l0 for all samples, most of the X-ray selected quasars are situated in'optically-faint regions of low luminosity. If we take lglo=31.2erg/s·Hz as a line of demarcation, and divide the optical luminosity into optically-bright and optically-faint regions, it is found that the radio and optically selected quasars have a slope of b=0.64 in the optically-bright region on this plot, and 6=0.95 in the optically-faint region, while the value of b of the X-ray selected quasars is only 0.78, thus implying that they may be a subtype of quasar phenomenon. Finally the factors affecting b are discussed briefly.