As an important branch of metamaterial-based devices, metamaterial absorber (MA) has aroused great interest and made great progress in the past several years. By manipulating the magnetic resonance and the electric resonance simultaneously, the effective impedance of MA will match the free space impedance, thus resulting in a perfect absorption of incident waves. Due to the advantages of thin thickness, high efficiency and tunable property, MA has been widely concerned in energy-harvesting and electromagnetic stealth. Since the first demonstration of MA in 2008, many MAs have been extensively studied in different regions, such as microwave frequency, THz, infrared frequency and optical frequency. At the same time, the absorber has been extended from the single-band to the dual-band, triple-band, multiple-band and broadband. In recent years, the dual-band absorber has received significant attention and has been widely studied. So far, however, most of MAs are composed of a bottom continuous metallic layer, which prevents electromagnetic waves from penetrating and makes electromagnetic waves absorbed or reflected. In this paper, an ultrathin flexible transmission absorber with a total thickness of 0.288 mm is designed and fabricated, which can be conformally integrated on an object with a curved surface. The absorber consists of three layers of structure: the bottom is a one-dimensional grating type metal line, the middle is the medium layer, and the surface metal layer is composed of two different sizes metal lines in parallel. Simulation and experimental results show that the absorptions of TE wave are 97.5% and 96.0% respectively at the two frequency points of 5 GHz and 7 GHz. The transmission of the TM wave above 90% is maintained from 3 GHz to 6.5 GHz. We also simulate the spatial electric field distribution and magnetic field distribution at two resonant frequencies, and explain the electromagnetic absorption mechanism of the proposed structure for TE wave. Secondly, when the incident angle increases to 60 degrees, the performance of the absorber is substantially unaffected, exhibiting good wide-angle characteristics. In addition, through the analysis of structural parameters, two absorption peaks of the proposed absorber can be independently adjusted, resulting in a flexible design. In conclusion, we propose both theoretically and experimentally a polarization-controlled transmission-type dual-band metamaterial absorber that can absorb the TE waves and transmit the TM wave efficiently, which has important applications in the case requiring bidirectional communication.