A new approach to reconstructing antenna far-field patterns from the missing part of the pattern is presented in this paper. The antenna far-field pattern can be reconstructed by utilizing the iterative Hilbert transform, which is based on the relationship between the real and imaginary part of the Hilbert transform. A moving average filter is used to reduce the errors in the restored signal as well as the computation load. Under the constraint of the causality of the current source in space, we could successfully reconstruct the data. Several examples dealing with line source antennas and antenna arrays are simulated to illustrate the applicability of this approach.