In this paper, a reversible simple air refrigeration cycle is studied by using classical thermodynamics, and the figures of merit proposed by finite time thermodynamics is used as the optimization objective. Through theoretical analysis and numerical calculations, the analytical formulas between figures of merit and influencing parameters are derived. By optimizing the pressure ratio, the optimal performance of the refrigeration cycle is given. The influence of cycle temperature ratio on the optimal performance of refrigeration cycle is analyzed. The results show that when the figures of merit is selected as optimization objective for performance optimization, there is an optimal pressure ratio to make the figures of merit get the maximum value. Moreover, the optimization results ensure the coordination between the cooling load and COP, which is a better compromise plan.