A novel, compact and multichannel nonreciprocal absorber through a wave tunnel- ing mechanism in epsilon-negative and matching metamaterials is theoretically proposed. Non- reciprocal absorption properties are acquired via the coupling together of evanescent and prop- agation waves in an asymmetric configuration, constituted of nonlinear plasma alternated with matching metamaterial. The absorption channel number can be adjusted by changing the pe- riodic number. Due to the positive feedback between nonlinear permittivity of plasma and the inner electric field, bistable absorption and reflection are achieved. Moreover, compared with some designs proposed before, our design is more compact and independent of incident angle or polarization. This kind of multilayer structure offers additional opportunities to design novel ormidirectional EM wave absorbers.