Transitions of laser diode (LD) pumped Er^(3 )-Yb^(3 ) co-doped glass laser are rather complicated. Considering energy transfer between Er^(3 ) and Yb^(3 ) ions, cross-relaxation, upconversion luminescence, and other transition processes, rate equations of quasi-three energy-level-system of the Er^(3 )-Yb^(3 ) co-doped laser are presented. The output characteristics are also calculated and analyzed in detail. The results show that Er^(3 )-Yb^(3 ) co-doped phosphate waveguide lasers with high slope efficiency and low threshold can be achieved.