We report a gradient metasurface design at microwave bands as an elegant approach to realize the goal of "rainbow trapping" for the storage of waves involving wave localization and absorption phenomena. A longitudinally placed coplanar waveguide is loaded with gradient metasurfaces on both sides, where split-ring resonators (SRRs) are the basic cell. The same SRRs are arranged along the transverse direction to establish magnetoinductive channels. Waves of different frequencies are coupled to corresponding SRRs at different positions in metasurfaces. Resonant trapping with a long oscillation life time enhances the absorption caused by inherent losses of the materials, thereby suppressing reflections. Both simulations and measurements verify the existence of "rainbow trapping." The proposed strategy enhances the interaction between waves and matter, opening an avenue for further component designs, including absorptive filters, multiplexers, and buffers.