The way how to reduce the induced drag in an aircraft design was researched and an inverse design method of geometric twist for the aircraft design was proposed to optimize its ratio of lift to drag. By defining the target circulation distribution, the method designed the geometric twists for controlled sections along the wing spanwise to implement the target distribution. A matrix expression for the integro-differential equations of Prandtls lifting-line theory described by Fourier sine series was established. Then, the aerodynamic calculation, aerodynamic spanwise distribution calculation and geometric twist angle inverse design were programmed and a geometric twist wing was designed to achieve elliptical spanwise distribution. Finally, the optimized results were simulated by the forecast of program and Computational Fluid Dynamic (CFD). The simulation results indicate that the lift spanwise distribution of twisted wing is elliptic, the induced drag and total drag are decreased by 17.07% and 15.43%, respectively, and the ratio of lift to drag is improved by 6.5%. This method aims at controlled sections, shows better realizability, and gives out a reference for engineering applications.