The pursuit of tunable asymmetric sound transmission has been a long-term topic since it could contribute to providing more flexibilities in many areas of acoustic engineering. The interference effect can be a feasible approach in which two waves with the same frequency superposed to form the resultant wave with manipulated amplitude according to the relative phase difference between them. However, strictly speaking, restricted by the spatial variance of phase, the manipulated domain created by the specific phase difference is always limited to a spot with dimensions much smaller than the wavelength. Here, we proposed a design to break this barrier that can realize the tunable asymmetric transmission via the combination of zero-index metamaterials and the binary metasurface. The zero-index metamaterial can provide the effective extremely large speed to shrink the infinite domain into a spot acoustically and the binary metasurface can be used to tune the specific phase difference. Numerical simulations and experimental measurements have good agreement and show that the acoustic waves impinged from the side of metasurface will be manipulated to have controllable transmission, while the acoustic waves impinged from the side of zero-index metamaterials will keep a high transmission. We think the proposed design is full of physical significance, which may find potential applications in many fields, like noise cancelation, acoustic imaging, and ultrasound therapy.