Abstract: When deriving the Fourier diffraction theorem based on the first-order Born approximation, the difference between wave number of the scattering object and that of the surrounding medium is ignored, causing substantial errors in sound scattering prediction. This paper modifies the Born approximation by taking into account the amplitude and phase changes at the interface between the scattering object and the water due to the wave number difference. By changing the radius and center position of the sampling circle in the Fourier domain, accuracy of the predicted sound scattering is improved. With the modified Born approximation, the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution. Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.