Optical metasurfaces consisting of single-layer nanostructures have immensely promising applications in wavefront control because they can be used to arbitrarily manipulate wave phase, and polarization. However, anomalous refraction and reflection waves have not yet been simultaneously and asymmetrically generated, and the limited efficiency and bandwidth of pre-existing single-layer metasurfaces hinder their practical applications. Here, a few-layer anisotropic metasurface is presented for simultaneously generating high-efficiency broadband asymmetric anomalous refraction and reflection waves. Moreover, the normal transmission and reflection waves are low and the anomalous waves are the predominant ones, which is quite beneficial for practical applications such as beam deflectors. Our work provides an effective method of enhancing the performance of anomalous wave generation, and the asymmetric performance of the proposed metasurface shows endless possibilities in wavefront control for nanophotonics device design and optical communication applications.