For millimeter-wave (mmWave) massive multiple-input-multiple-output (MIMO) systems, codebook-based analog beamforming (including transmit precoding and receive combining) is usually used to compensate the severe attenuation of mmWave signals. However, conventional beamforming schemes involve complicated search among predefined codebooks to find out the optimal pair of analog precoder and analog combiner. To solve this problem, by exploring the idea of turbo equalizer together with the tabu search (TS) algorithm, we propose a Turbo-like beamforming scheme based on TS, which is called Turbo-TS beamforming in this paper, to achieve near-optimal performance with low complexity. Specifically, the proposed Turbo-TS beamforming scheme is composed of the following two key components: 1) Based on the iterative information exchange between the base station (BS) and the user, we design a Turbo-like joint search scheme to find out the near-optimal pair of analog precoder and analog combiner; and 2) inspired by the idea of the TS algorithm developed in artificial intelligence, we propose a TS-based precoding/combining scheme to intelligently search the best precoder/combiner in each iteration of Turbo-like joint search with low complexity. Analysis shows that the proposed Turbo-TS beamforming can considerably reduce the searching complexity, and simulation results verify that it can achieve near-optimal performance.