This paper represents a numerical study of a triple-stage series flow absorption cycle operating with LiBr-H2O pair. A computational model is implemented using Engineering Equation Solver (EES) software. This model includes equations of mass, species and energy conservation. The analysis is used to simulate a triple stage absorption chiller utilization for an air conditioning applications with a nominal capacity of 300kW manufactured by Thermax company. This chiller is indirect fired type which uses steam from boiler of the HPG as heat source. The variations of performance parameters with different ranges of operation conditions have been calculated. The operating parameters are selected as follows: the HPG, MPG and LPG temperatures: THPG= 150-230°C, TMPG= 100-130°C and TLPG= 60-95°C, respectively, LPC temperature TLPC= 28-37°C, evaporator temperature Tevap = 5-14°C; flow rate of refrigerant mr= 1 kg/s; four values of heat exchangers effectiveness 0.4, 0.5, 0.6 and 0.65. In addition, the comparison between the present study and other study obtained in literature review has been done. The analysis revealed that maximum COP is found as a function of both MPG and LPG temperatures. The results outline that the COP increases with an increase in the evaporator and generators temperature but decreases with condenser temperature.