In order to improve the quality of the received signal and system spectral efficiency, accurate beamforming using a given antenna array is essential for multiple-input multiple-output (MIMO) systems. To obtain desired MIMO transmission performance, construction of codebooks which are composed of matching beamforming vectors to the array structure is important. To effectively cover different types of mobile traffic, the base station for 5G new radio employs antenna arrays in various sizes and shapes. Nevertheless, the codebooks adopted by the 3GPP standard so far are based on the uniform linear array and the uniform planar array, necessitating design techniques for a wider class of antenna arrays. In this paper, we propose codebook construction methods for the uniform circular array with parameters to flexibly set the initial phase and step size based on the channel characteristics of the user equipment (UE). When tested over the 3GPP spatial channel model, the proposed codebooks show a substantial amount of gain over the conventional codebooks in all UE locations within the cell.