We theoretically design and numerically demonstrate an acoustic one-way metasurface, which is a planar and acoustically subwavelength layer behaving like a nearly-reflectionless surface with arbitrary wave-steering capability for incident wave impinging on one side, while virtually blocking the reversed wave. The underlying mechanism is based on an asymmetric phase modulation by coupling a phase array and a near-zero-index medium. We exemplify a metastructure-based implementation by combining the hybrid metastuctures and labyrinthine structures. Moreover, the performance of the proposed implementation is demonstrated via three distinct phenomena of anomalous refraction, wave splitting and conversion of propagation wave to surface wave. Our findings may offer more possibilities for sound manipulation and improve the application potential of acoustic artificial devices in situations such as ultrasonic imaging and therapy.