Aim of this study is to investigate an aerodynamic effect of a drag-reducing device on a heavy-duty truck. The vehicle experiences two different kinds of aerodynamic forces such as drag and uplifting force (or downward force) as it is traveling straight forward at constant speed. The drag force on a vehicle may cause an increase of the rate of fuel consumption and driving instability. The rolling resistance of the vehicle may be increased as result of the negative uplifting or downward force on the vehicle. A device named roof-fairing system has been applied to examine the reduction of aerodynamic drag force on a heavy-duty truck. As for a engineering design information, the drag-reducing system should be studied theoretically and experimentally for the best efficiency of the device. Four different types of roof-fairing model were considered in this study to investigate the aerodynamic effect on a model truck. The drag and downward force generated by vehicle has been obtained from numerical calculation conducted in this study. The forces produced on four fairing models considered in this study has been compared each other to evaluate the best fairing model in terms of aerodynamic performance. The result shows that the roof-fairing mounted truck has bigger negative uplifting or downward force than that of non-mounted truck in all speed ranges, and drag force on roof-fairing mounted truck has smaller than that of non-mounted truck. The drag coefficient $(C_D)$ of the roof-fairing mounted truck (Model-3) is reduced up to $41.3\%$ than that of non-mounted trucks (Model-1). A downward force generated by a roof-fairing mounted on a truck is linearly proportional to the rolling resistance force. Therefore, the negative lifting force on a heavy-duty truck is another important factor in aerodynamic design parameter and should be considered in the design of a drag-reducing device of a tractor-trailer. According to the numerical result obtained from present study, the drag force produced by the model-3 has the smallest of all in all speed ranges and has reasonable downward force. The smaller drag force on model-3 with 2/3h in height may results of smallest thickness of boundary layer generated on the topside of the container and the lowest intensity of turbulent kinetic energy occurs at the rear side of the container.