In this Communication, we provide an efficient algorithm for the evaluation of the semi-infinite array Green's function (SAGF) for a semi-infinite planar periodic phased array of dipoles in free space. For observation points not too far from the array plane, the algorithm uses a hybrid spectral-spatial representation of the Green's function accelerated with the Levin T method, that we show to be faster than the Shanks method. For observation points sufficiently far away from the array plane, we show that the SAGF is efficiently evaluated by using asymptotic field expressions. Asymptotics is also used to explain the loss of accuracy of the Levin T accelerator in certain regions, and a correction procedure is proposed to overcome this problem. © 2006 IEEE.