A narrow-band and high-contrast asymmetric transmission (AT) device based on metal-metal-metal (M-M-M) asymmetric grating structure is proposed and investigated. Significantly distinct from previous reports, the upper and lower metallic silver (Ag) gratings are connected by a very thin metallic Ag film, without any dielectric spacer layer or subwavelength slit. Under forward incidence, the M-M-M structure supports efficient surface plasmon polaritons (SPPs) excitation and tunneling, more importantly, it promotes direct and thus high-efficiency SPPs decoupling, enabling high forward transmittance. While under backward incidence, the M-M-M structure offers not only high reflection by the Ag film but also a strong near-field coupling effect between the upper and lower gratings, which further suppresses backward transmittance, leading to near-zero backward transmittance. In addition, the M-M-M structure is optimized for narrow-band operation by employing grating groove depth effect and multiple interference effect. Numerical simulation results demonstrate that high-performance AT with high-quality factor (Q≈91), narrow-bandwidth (6.7 nm) and high contrast ratio is achieved, with forward transmittance of 0.72 and backward transmittance of 0.0015 at visible light (610 nm). Our work provides an alternative and simple way to high-performance AT devices.