To address the environmental impact of air travel, the industry has introduced various solutions, including sustainable fuels and new aircraft configurations. The Flying V is one such concept that promises a 20% reduction in fuel consumption compared to its most advanced competitor. Unlike traditional commercial airplanes, the Flying V is a tailless flying-wing design without a tubular fuselage, horizontal, and vertical tailplane, using elevons and winglets featuring rudders for control. This study aimed to optimize the wing geometry of the Flying V aircraft to minimize induced drag under specific subsonic conditions (M = 0.6) and a given lift coefficient of 0.26. The approach combined a Vortex Lattice Method (VLM) with an optimization algorithm, specifically using the Athena Vortex Lattice (AVL) software for aerodynamics calculations. A low-fidelity method, such as a VLM, allows a faster and deeper exploration of the design space than a high-fidelity method like Computational Fluid Dynamics (CFD). To improve the Flying V's design, a simpler parameterization was introduced to represent the complex model of the Outer Mold Line (OML) of the aircraft. It involved eight sections along half the wingspan. The inboard wing sections were parameterized in a wire-frame style, with the front part representing the location of the passengers' cabin, requiring fixed dimensions and inclination to accommodate a suitable cabin floor, and the aft part allowed to be rotated. The other sections' geometry was mainly described by the total inclination angle. The design vector included the aft angles of the first three sections, the total incidence angle of the last four sections, and the dihedral of the outboard wing, which is useful to ensure a straight hinge line for control power. A total of 8 design variables were utilized during the optimization process. Two aerodynamic constraints were implemented to ensure feasible optimized results. The first constraint was related to the resulting angle of attack computed by AVL based on the defined geometry and lift coefficient input. Such constraint was necessary to control the total inclination of the passengers' cabin during cruise. The second constraint was imposed as a measure to control the aircraft's stability margin. In addition, a simplified empirical viscous module was introduced to get a better estimation of the total lift-to-drag ratio and a sensitivity analysis was performed to assess the impact of each variable on the model’s output. The final design showed a 4.38% increase in lift-to-drag ratio compared to the initial design and a 10.5% reduction in induced drag coefficient. Furthermore, the optimized lift distribution showed an averaged elliptical shape with respect to the initial design. This showcases the significant enhancements achieved in the aerodynamic performance of the optimized configuration.