The present paper describes the optimum inverse design of 2-D linear cascade airfoil. The pressure coefficient of an airfoil surface is taken as the objective function, and non-orthogonal incompressible Navier-Stokes equation is applied to calculate the pressure coefficient. Both of steepest descent and conjugate gradient method have been used to make the objective function go to zero. The 1st order finite differential method is applied to the searching direction and the golden section method is used to compute the searching distance. As a result of the present work, a good convergence to the target airfoil has been obtained.