In this paper, we study full-dimension multiple-input multiple-output (FD-MIMO) systems where a base station is equipped with multiple panel array (MPA) antennas. As the MPA is regarded as a promising means of practical implementation for the FD-MIMO, it is important to characterize a channel modeling and a codebook design. Thus, we first examine the exponential correlation model and the three-dimensional correlation model for the FD-MIMO with MPA. In addition, since antenna elements are not uniformly spaced in the MPA systems, a discrete Fourier transform (DFT) codebook may not be suitable due to phase ambiguity (PA). Thus, we investigation three new codebook design methods which reflect the PA. In numerical results, we confirm that PA compensation and per-panel quantization are effective for MPA systems.