In this paper, auxiliary beam pair design is developed to provide high-resolution estimates of channel's elevation/azimuth angle-of-departure (AoD) and angle-of-arrival (AoA) for millimeter- wave full-dimension MIMO (FD-MIMO) systems. Pairs of custom designed analog beams are formed at both the transmitter and receiver to help acquire channel information. It is shown via simulation results that by employing the proposed method, promising elevation/azimuth AoD and AoA estimation performance can be achieved under various signal- to-noise ratio levels and channel conditions.