Metastructures can be designed to exhibit extraordinary properties and thus are widely applicable in various fields, such as vibration suppression, wave control, and energy harvesting. In the present work, a dynamic homogenization model is strictly derived for a metabeam (a beam with periodic resonators) by using the asymptotic homogenization method. The homogenization model is validated via comparing the vibration frequencies and associated vibration modes of the metabeam predicted by the present model with exact ones, and it is then used to analyze the linear (or nonlinear) vibration responses of the metabeam subject to a harmonic excitation with a small- (or large-) amplitude. Furthermore, the effect of periodic resonators on the vibration suppression performance of the metabeam is discussed. It is demonstrated that such kind of dynamic homogenization model is of great convenience to predict the vibration responses of metastructures besides the widely studied dispersion relation. Thus, it is expected to be useful for the vibration suppression and control of engineering structures.