In this study, the performance evaluation of an adsorption chiller (AD) system with three different adsorbents—silica-gel, aluminum fumarate, and FAM-Z01—was conducted to investigate the effects of adsorption isotherms and physical properties on the system’s performance. In addition, the performance evaluation of the AD system for a low inlet hot-water temperature of 60 °C was performed to estimate the performance of the system when operated by low quality waste heat or sustainable energy sources. For the simulation work, a two-bed type AD system is considered, and silica-gel, metal organic frameworks (MOFs), and ferro-aluminophosphate (FAPO, FAM-Z01) were employed as adsorbents. The simulation results were well matched with the laboratory-scale experimental results and the maximum coefficient of performance (COP) difference was 7%. The cooling capacity and COP of the AD system were investigated at different operating conditions to discuss the influences of the adsorbents on the system performance. Through this study, the excellence of the adsorbent, which has an S-shaped isotherm graph, was presented. In addition, the influences of the physical properties of the adsorbent were also discussed with reference to the system performance. Among the three different adsorbents employed in the AD system, the FAM-Z01 shows the best performance at inlet hot water temperature of 60 °C, which can be obtained from waste heat or sustainable energy, where the cooling capacity and COP were 5.13 kW and 0.47, respectively.