An analytical model of passively Q-switched diode-pumped Er-Yb:glass laser with a Co2+:MgAl2O4 plate as a saturable absorber has been developed. Considering energy transfer between Er3+ and Yb3+, upconversion luminescence and the transition processes of the Co2+ in the Co2+:MgAl2O4 plate, rate equations of the passively Q-switched laser are presented and useful conclusions are drawn by numerical analysis in the paper. The model is very useful for optimizing these kind of lasers.