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This work demonstrates a two-dimensional (2D) bilayered metamaterial that exhibits dual-band asymmetric transmission (AT) effect for linear polarization. The measured cross-polarization transmissions are 0.88 at 5.68 GHz and 0.92 at 10.7 GHz in one direction, while the corresponding cross-polarization transmissions are suppressed down to 0.17 and 0.18 in the opposite direction, and the AT parameters Δx/Δy reach 0.73/−0.73 and 0.80/−0.80 respectively. The simulated surface current distributions reveal that the underlying physics originates from the induced magnetic coupling. The simulated resonant electric/magnetic field distributions show that the proposed structure follows the principle of metamaterials’ subwavelength.