Though metamaterials enhance nonlinear light-matter interactions due to their resonant features, these materials typically show a narrow spectral bandwidth. Here, the authors report broadband enhanced second-harmonic generation in patterned multilayer hyperbolic metamaterial arrays. Metasurfaces have provided a promising approach to enhance the nonlinearity at subwavelength scale, but usually suffer from a narrow bandwidth as imposed by sharp resonant features. Here, we counterintuitively report a broadband, enhanced second-harmonic generation, in nanopatterned hyperbolic metamaterials. The nanopatterning allows the direct access of the mode with large momentum, rendering the rainbow light trapping, i.e. slow light in a broad frequency, and thus enhancing the local field intensity for boosted nonlinear light-matter interactions. For a proof-of-concept demonstration, we fabricated a nanostructured Au/ZnO multilayer, and enhanced second harmonic generation can be observed within the visible wavelength range (400-650 nm). The enhancement factor is over 50 within the wavelength range of 470-650 nm, and a maximum conversion efficiency of 1.13x10(-6) is obtained with a pump power of only 8.80 mW. Our results herein offer an effective and robust approach towards the broadband metasurface-based nonlinear devices for various important technologies.