The recent reported trapped ''rainbow'' storage of light using metamaterials and plasmonic graded surface gratings has generated considerable interest for on-chip slow light. The potential for controlling the velocity of broadband light in guided photonic structures opens up tremendous opportunities to manipulate light for optical modulation, switching, communication and light-matter interactions. However, previously reported designs for rainbow trapping are generally constrained by inherent difficulties resulting in the limited experimental realization of this intriguing effect. Here we propose a hyperbolic metamaterial structure to realize a highly efficient rainbow trapping effect, which, importantly, is not limited by those severe theoretical constraints required in previously reported insulator-negative-index-insulator, insulator-metal-insulator and metal-insulator-metal waveguide tapers, and therefore representing a significant promise to realize the rainbow trapping structure practically. S low-light chips are believed to be promising for enhanced optical buffering, signal processing, and enhanced nonlinear optics. Unfortunately, the observation of slow light in conventional schemes based on BoseEinstein condensates 1 or atomic vapors 2 imposes severe constraints in experimental conditions, including narrow bandwidth, limited working wavelengths and strong temperature dependence. The slowed modes are difficult to be implemented into other materials or devices to develop practical applications. Consequently, solidstate nanophotonic structures that can achieve the slow light effect under room temperature are of particular interest [3][4][5] . Recent theoretical and experimental investigations on the ''trapped rainbow'' storage of light waves in metamaterials 6 and plasmonic structures 7-10 have generated considerable interest since various solid-state materials can be introduced in the design of nanostructures to trap electromagnetic (EM) modes. With the ability to produce highly confined and localized optical fields, it is believed that the conventional rules for light-matter interactions need to be re-examined, and new regimes of optical physics are expected. To develop applications based on this intriguing broadband slow light effect, various architectures have been proposed, including surface graded metallic gratings 9,10 , insulator-negative-index-insulator (INI) 6,11 , insulator-metal-insulator (IMI) 12 and metal-insulator-metal (MIM) waveguide tapers [13][14][15] . However, each proposal has its inherent difficulties resulting in the limited experimental realization of the rainbow trapping structures. For example, in our previous experimental reports, white light surface plasmon polariton (SPP) modes were launched into the on-chip gratings through nanoslits 9,10 , leading to a very weak total coupling efficiency. For INI waveguide tapers, there is currently no clear pathway for realizing materials with negative refractive indices over a broad spectral range 6 . In a recent theoretical investigation...