A gradient based aerodynamic optimizer has been built for nozzle inverse design problem. Solution sensitivity at nozzle walls is calculated using the analytic solution of quasi one dimensional nozzle flow while the flow field solution is computed using CFD finite volume solver. The gradient of the inverse design objective function is computed using the solution sensitivity at nozzle walls which is computed analytically, and using also the computed Mach distribution resulting from CFD simulation. As the nozzle wall contour changes during optimization iterations; we used linear spring mesh movement analogy to adapt the mesh grid points in the entire flow field to the new nozzle contour shape. A supersonic inverse design test case is presented and it shows the success of the proposed method as an aerodynamic design and optimization technique.