This paper proposes an efficient low-speed airfoil selection and design optimization process using multi-fidelity analysis for a long endurance Unmanned Aerial Vehicle (UAV) flying wing. The developed process includes the low speed airfoil database construction, airfoil selection and design optimization steps based on the given design requirements. The multi-fidelity analysis solvers including the panel method and computational fluid dynamics (CFD) are presented to analyze the low speed airfoil aerodynamic characteristics accurately and perform inverse airfoil design optimization effectively without any noticeable turnaround time in the early aircraft design stage. The unconventional flying wing UAV design shows poor reaction in longitudinal stability. However, It has low parasite drag, long endurance, and better performance. The multi-fidelity analysis solvers are validated for the E387 and CAL2463m airfoil compared to the wind tunnel test data. Then, 29 low speed airfoils for flying wing UAV are constructed by using the multi-fidelity solvers. The weighting score method is used to select the appropriate airfoil for the given design requirements. The selected airfoil is used as a baseline for the inverse airfoil design optimization step to refine and obtain the optimal airfoil configuration. The implementation of proposed method is applied for the real flying-wing UAV airfoil design case to demonstrate the effectiveness and feasibility of the proposed method.