A general computational method is proposed to evaluate aerodynamic noise generated by unsteady flows interacting with non-compact boundary. Firstly, a boundary element method is applied to compute the exact/tailored Green’s Function that satisfied the specific boundary conditions. Then, the numerical results of exact/tailored Green’s Function are used to solve FW-H equation to predict the far field noise. This numerical method can predict not only the radiating noise from the aerodynamic sources, but also the scattering noise from non-compact surfaces. Especially, the approach is suitable for boundary which has large and complex geometric shape. The present method is applied to predict aerodynamic noise generated by turbulent flows at Reynolds number of 90000 over a circular cylinder with non-compact boundary conditions.