In this work, Harmony Search Meta-Heuristic Optimization Algorithm has been developed for aerodynamic shape optimization problem for the first time. The aerodynamic shape, which has been investigated, is an airfoil with Parces method for its shape parameterization. The problem was minimization of aerodynamic objective function using inverse design method and the objective function has been the deviation of pressure distribution between investigated airfoil and the target airfoil. The 2-Dimensional compressible Navier-Stokes equations have been considered for simulation of flow using Spalart-Almaras turbulence model. A global improvement has been carried out to enhance the efficiency of Harmony Search Algorithm. In improved Harmony Search Algorithm one obtains the optimum design values and target airfoil by changing the airfoil shape design variables. To do this, algorithm starts from NACA0012 airfoil and reconstructs the target airfoil (RAE2822) by making pressure distribution closer to the target airfoil pressure distribution. For more accurate investigation and to make sure about the accuracy of algorithm, this optimization process has also been done in inverse direction. It means that, NACA0012 airfoil has been reconstructed starting from RAE2822 airfoil. The obtained results show that the utilization of Harmony Search Algorithm allows us to obtain an efficient and powerful tool for Aerodynamic Shape Optimization.