Abstract: Far-field antenna measurement is a traditional method to obtain antenna radiation characteristics. In order to analyze the details of the radiation pattern, the angular interval of the measured radiation pattern should generally be less than 1/10 of the half-power beam width of the antenna under test, otherwise it may introduce errors to the antenna radiation parameters (half-power beam width, sidelobe level, etc.). For the far-field measurement of a high-gain, narrow-beam antenna, in order to obtain accurate results, the measurement interval should be very small, leading to long measurement time and reducing measurement efficiency. High efficiency antenna measurement of Fourier interpolation method based on band-limited periodic function is given in this paper and has been used in practical antenna measurement. Using the proposed method, the sampling interval can be increased to the order of the half-power beam width of the antenna under test, and the radiation pattern of arbitrarily small angular intervals can be reconstructed accurately, which can significantly improv the measurement efficiency. Simulated and measured results prove effectiveness of the algorithm.