Different from the conventional metamaterial absorbers (MAs), which used metal resonance surface and ternary structure (metaldielectric-backplane), as an alternative route, the all-dielectric resonance surface (ADRS) made of single low-permittivity dielectric is proposed to design binary (dielectric backplane) metamaterial absorber (BMA). As an illustration, a triple-band BMA composed of ADRS with a metallic backplane is designed and fabricated, where the ADRS incorporates two dielectric layers with different hole-array structures. The absorbing mechanisms of this kind of absorber are analyzed via analyzing configurations of power loss density, electric field and magnetic field, as well as investigating dependences of absorbing properties on structure dimensions. The study indicates that the structural design of ADRS leads to reverse magnetic field rings distributed inside the dielectric, forming the strong couplings at the resonance frequencies. The proposed BMA relies on low-permittivity ADRS, with the rapid preparation and low cost greatly simplifying the design of MAs. The current concept is also suitable to design multi-band and broadband MAs worked at other bands, by changing the structural design of ADRS.