This paper adopts an investigation of a novel cascading adsorption cooling system. The system has two high-temperature zeolite-water beds topping a silica-gel/water bed using the heat recovery technique. A parametric study is carried out on the proposed method using a robust numerical model that shows excellent validation compared to the data reported in the literature. The system is assessed using two performance indices: the specific cooling power (SCP) and the coefficient of performance (COP). The results indicate that the proposed system has a COP value approaching 1.6, and its SCP can reach 170 W/kg. It is observed that increasing the half-cycle time of zeolite beds from 10 to 120 min reduces the SCP by 80% while it increases the COP by about 53%. In this regard, it is noticed that a half-cycle time of 60 min is recommended for optimal system performance. When the heating source temperature increases (110–190 °C), a rise of 120% is obtained in the SPC and COP enhances by about 35%. Above this temperature level, the increase in the SPC becomes unnoticeable, and conversely, the COP slightly drops. Moreover, when the bed's cooling-fluid inlet temperature to the system rises from 10 to 40 °C, there is a forty percent decline in SCP with a thirty percent drop in the COP. In this regard, it is preferable to keep the bed's cooling-fluid inlet temperature below 30 °C for better performance. Also, the mass flow rate of the cooling fluid shouldn't be less than 0.1 kg/s. An increase in the inlet temperature of chilled water (5–25 °C) leads to increases in the SCP and COP by 200 and 65%, respectively. Moreover, the SCP and COP decline by 70 and 30% when the total zeolite mass rises from 2 to 30 kg. For better system performance, the ratio of the silica-gel mass to the total zeolite mass in the system should range from 0.45 to 0.55.