For a decade, the acoustic cloak has attracted considerable research interests. Meanwhile, the effect of mean flow on the scattering pattern from acoustic cloak was rarely explored. As reported by previous investigations on the acoustic cloak in flow field, the existing cloak designs fail to preserve its original properties to make an object acoustically invisible. Recently, the authors studied that the failure reason of acoustic cloak is mainly due to effects of compressibility in fluid and non-uniformity of flow. Thus, to improve the performance of conventional acoustic cloak, we focused on how to suppress non-zero gradient of flow velocity. When we performed the numerical simulations for various thicknesses of acoustic cloak, the thinner acoustic cloaks had better performance than the thicker ones. This work is expected to provide an insight toward a design of perfect acoustic cloak in moving medium.