This paper presents the computational aerodynamic analysis of a long-endurance UAV that was developed by the Korea Aerospace Research Institute (KARI), named EAV-2. EAV-2 is a technical demonstrator of aerodynamically efficient design, as well as a hybrid electric-propulsion system for future long-endurance UAVs. We evaluated the aerodynamic characteristics of six low-Reynolds number airfoils, using a panel method code, XFOIL, to select an optimal airfoil for the long-endurance mission of EAV-2. The computational results by a CFD code, FLUENT, suggested that the aerodynamic performance of EAV-2 would be notably improved after adopting SG6043 airfoil, and modifying the fuselage design. This reduced the total drag by 43%, compared to that of a previous KARI model, EAV-1, at the target lift of $C_L=1.0$. Also, we achieved a drag reduction of approximately 14% by means of the low-drag fuselage configuration.