A new type of multi-layer metamaterial (MM) absorber is represented in this paper, which behave as a dielectric slab in transmission band and act as an absorber in another lower band. The equivalent circuit model of each layer in this MM absorber has been established. The transmission line (TL) model is introduced to analysis the mechanism of electromagnetic wave traveling through this MM absorber. Both theoretical and experimental results indicate this MM absorber has a transmission band at 21GHz and an absorptive band from 5GHz to 13GHz. A good match of TL model results and measurement results verified the validity of TL model in analyzing and optimizing the performances of this kind of absorber.