In this paper a solar absorption cooling system with chilled water storage tank and peak load compression system was considered for cooling of the Instituto Superior Tecnico (IST) Tower building in Lisbon, Portugal. In order to do this task, a dynamic simulation of the building was performed using the DesignBuilder software, then a solar collector field was designed. The next step was to build a computational model of the absorption chiller in the Engineering Equation Solver software, which allowed for further simulation of the annual operation of the system supported by the chilled water tank and the backup system with compressed air conditioning. The last stage of the work was the economic analysis of such a system in comparison with conventional compressed air conditioning. The simulation results and economic analysis showed that the solar absorption cooling system could be a beneficial cooling solution for IST Tower building. However, it would have to operate with an energy storage system and a peak load compression backup system to be able to cool the building efficiently all year round. Additionally, such a solution could have a significant positive impact on climate through considerable annual savings in electricity consumption. Results revealed that the proposed system meets the cooling demand of the building, mainly by solar energy driven absorption chiller. The annual contribution of backup compression chiller ranges from 20% to 36% depending on the size of chilled water storage tanks. Financial calculations revealed discounted payback periods in the range of 4.5 to 11.2 years depending on system configuration.