This paper describes the theoretical prediction, simulation research, and experimental verification conducted to understand the potential of finite cylindrical micro-perforated panel absorbers (FC-MPPAs) in noise control. The simplified Rayleigh integral method is extended to predict the dissipation of sound energy in cylindrical micro-perforations with sub-millimeter aperture. The sound absorption and insulation performance of a FC-MPPA and the influence of its structural parameters on its acoustic performance were studied by model simulation and experiment, and the directional distribution of the sound field was revealed. The simulation and experimental results show that the FC-MPPA has unique acoustic characteristics different from the panel-type absorber, and its structural parameters are closely related to the acoustic-energy dissipation efficiency. Moreover, the absorption coefficient of FC-MPPA is a function of the incidence angle and frequency of the sound wave, and its acoustic properties are controlled by the coupling between the micro-perforated panel and the acoustic modes in the annular cavity domain. These studies can provide help in the design and application of FC-MPPA to achieve better noise reduction effect.