A new computer generated holography (CGH) algorithm based on Fourier transform is proposed. The complex amplitude of the light wave to be recorded is extended to produce a conjugate symmetric function. The function is then Fourier transformed to generate a real valued distribution containing both the amplitude information and the phase information of the light wave. The obtained real distribution is coded to give a gray-scale hologram，which can be used to reconstruct the original light wave. Unlike the existing CGH algorithms based on interference of object and reference light waves，the proposed method does not require simulatingthe interference to produce the hologram. The algorithm is highly efficient，and can produce good results both in digital and electroholographic reconstruction. Theoretical and experimental results are presented to verify the validity of the method.