Orbital angular momentum (OAM) carried by acoustic vortex attracts extensive research interests due to the possible application such as acoustic tweezer and communications. The OAM in the conventional symmetric acoustic vortex is generally determined by topological charge l. Here, we provide the beam symmetry as an alternative factor to manipulate the OAM beyond the topological charge. We propose a nondiffractive asymmetric acoustic vortex beam, which can be generated by an acoustic metasurface and modulate the OAM to arbitrary values. Rather than the radially symmetric distribution, the intensity of the asymmetric acoustic vortex is characterized with a crescent shape controlled by the asymmetry parameter $\ensuremath{\alpha}$. The ratio between axial OAM and sound energy on the transverse plane depends on the asymmetry parameter and thus is not quantized by the ratio of topological charge l to wave angular frequency $\ensuremath{\omega}$ as in conventional vortex beam. Moreover, we present the realization of the proposed vortex beam by designed metasurface, and reveal the nondiffractive nature of the asymmetric acoustic vortex beam. Our work expands the family of acoustic vortex and demonstrates an alternative route to control acoustic OAM.