We numerically and experimentally realize broadband acoustic focusing lenses by employing units of phase manipulation composed of different numbers of cavity structures immersed in air, which is different from other units of phase manipulation by adjusting the structural parameters. The phase delays of transmitted units could cover a whole 2π range by using six cavity structures. Based on these units, we design a transmitted acoustic lens with different focal lengths, and the working bandwidth could reach about 2.1 kHz. Besides, the influence of air attenuation on the focusing performance and of the inclined angles of the channels in the cavity structure on the phase delays are discussed in detail. Moreover, we realize a transmitted acoustic lens with two types of units, a reflected acoustic lens and a three-dimensional transmitted acoustic lens. Compared with other acoustic lenses, the proposed acoustic lenses have the advantages of broad bandwidths, high focusing performance, easy fabrication, and high robustness, which have great potential applications in airborne acoustic focusing devices.