Anisotropic superhydrophobic surfaces that have many superior properties, such as directional self-cleaning, droplet transport, heat transfer, and so on, are widely used in various fields. Different from symmetric surfaces, a water droplet often shows directional spreading, moving, and bouncing on asymmetric surfaces. To investigate the mechanisms and achieve controllability of droplet motions on asymmetric surfaces, a series of surfaces with inclined micro-conical arrays are fabricated by integrating the methods of soft lithography, hot-pressing, and crystal growth. We found that the droplet would spread along the reverse direction of micro-cone's orientation but bounce and detach off the surface and move toward the direction of micro-cone's orientation. To understand these interesting performances, a mathematical model is established from the perspective of force balance, and a series of numerical simulations are performed. Additionally, the relationship between the droplet motions and the micro-structural parameters, including the inclined angle, line space, and height, are studied. This work may provide useful insights into droplet controlling, anisotropic surface designing, and its applications.