Abstract: he array antennas with predetermined beam shapes have applications in the fields of satellite communication, remote sensing and synthetic aperture radar (SAR), etc. A new algorithm for array synthesis based on inverse Discrete Fourier Transform (IDFT) is proposed in the paper. This algorithm has the advantages of minor calculation and best calculating stability. It can make a flexible trade--off between the shaping accuracy in the main-lobe and the magnitude of the minor-lobes if a window function is used.