Patterned surfaces with rationally designed nanostructures provide a flexible platform for beam shaping in both the linear and nonlinear optical regime. The properties of reflected or diffracted output depend on the Fourier transform of the surface profile. To obtain ideal effects, the profile should contain a desired sum of specially formed sinusoidal terms with predefined superposition coefficients. Such a kind of surface is vividly described as a "wavy" surface in certain contexts, which has been widely utilized for linear optical applications. However, the nonlinear counterparts are rarely demonstrated. Here, we present a design framework of nonlinear "wavy" surfaces based on hybrid nanostructures of metal and multi-quantum-well (MQW) for generating and steering second-harmonic beams. Giant second-order nonlinearity is available in MQWs; thus, an efficient up-conversion process can be ensured. In this system, the harmonic output is determined by the Fourier spectrum of spatially dependent secondorder nonlinearity, which can be engineered through tailoring the shape, orientation, and arrangement of nanoelements known as "meta-atoms". Compared with previously proposed nonlinear metasurfaces, the wavy design can be more flexible for manipulating orbital angular momentum (OAM) states through introducing topological defects. Besides choosing states with expected topological charges and controlling the relative weight, the rule in conventional binary χ (2) systems that the attached OAM value increases with the order of reflection/diffraction can be broken via suitable nanostructure design, which means that lower order is possible to have larger absolute topological charge. This proposed framework has tremendous potential for applications in emerging areas such as quantum nanophotonics and topological photonics.