Codebooks with small inner-product correlation have applied in direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks achieving the Welch bound or the Levenstein bound. This paper focuses on constructing asymptotically optimal codebooks with characters of cyclic groups. Based on the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are presented. In addition, parameters of these codebooks are new.