Multi-pass solar air heater is attributed to the increase in efficiency due to reduce top heat loss. In this paper, a quadruple-pass solar air heater equipped with longitudinal fins on both sides of an absorber plate was investigated for efficiencies and axial temperature distribution. A mathematical model is formulated in form of ordinary differential equation (ODE) from eight heat transfer equations to solve for four local temperatures of airflow and four local temperatures of surfaces (two glass covers and two absorber plates). ODEs are solved by numerical integration and validated by the comparison with the published data. The current approach is conducted since an analytical model and parametric study on quadruple-pass solar air heater has not been found in the open literature. Among the fin parameters including thickness, quantity, and height, the fin height has a great influence on thermal efficiency. Thermal efficiency can reach 65.7% at maximum fin height. Reynolds number of 5500 achieves maximum effective efficiency of 63.5%. When the Reynolds number is large, heat transfer in the fourth pass is poor due to the sharp drop in surface temperature at high airflow rate.