Two-photon absorbing alkali vapor laser (TPAL) has important application prospects in basic research and defense engineering, and has become one of the research hotspots in the laser field in recent years. However, TPAL still lacks relevant theoretical models. The operating characteristics of a single-wavelength pumped two-photon absorbing rubidium vapor laser (Rb-TPAL) are investigated, and the effects of pump beam waist position, vapor cell temperature and pump power on the blue light output characteristics of Rb-TPAL are analyzed. The results show that the optimal pump beam waist position and vapor cell temperature exist for the Rb-TPAL to output the highest power blue laser. By optimizing the pump beam waist position and vapor cell temperature, the Rb-TPAL can obtain high power blue laser output under high power pumping.