In this work, the development of a conceptual design methodology of an innovative aircraft configuration, known as box wing, is presented. A box wing aircraft is based on a continuous-surface nonplanar wing formation with no wing-tips. The A320 medium range conventional cantilever wing aircraft is used as both the reference aircraft and the main competitor of the box wing aircraft. Based on the A320 characteristics and dimensions, a complete aerodynamic analysis of the box wing configuration is made by means of layout design and computational fluid dynamics studies, highlighting the aerodynamic and operating advantages of the box wing configuration compared to the A320 aircraft. The aspect ratio and the Oswald factor of a box wing aircraft differ significantly from the corresponding ones of A320 and provide increased aerodynamic performance. The increased aerodynamic performance leads by consequence, to lower fuel consumption, thus allowing longer range for the same payload or greater payload for the same range, contributing to the efforts for greener environment. In this work, the design methodology begins by estimating the critical initial design parameters, such as aspect ratio, dihedral angle, sweep angle, and taper ratio, which are continuously refined via an iterative process based on a conceptual design study. Various flying scenarios are studied using computational fluid dynamics and analytical calculations, in order to compare the performance of the box wing and the conventional A320, having always the same mission and payload conditions. The conceptual results show that the novel box wing configuration has considerable aerodynamic performance advantages compared to the conventional A320 aircraft.