The effective removal of uranium from an aqueous solution is a highly valuable process for the environment and health. In this study, we developed a facile and rapid method to synthesize hierarchically porous Cu-BTC (RT-Cu-BTC) using a cooperative template strategy. The as-synthesized RT-Cu-BTC exhibited hierarchically porous structure and excellent thermostability, as revealed by X-ray powder diffraction, Fourier-transform infrared spectroscopy, scanning electron microscopy, and thermogravimetric analysis. Compared with conventional metal–organic frameworks (MOFs) and zeolites, the obtained RT-Cu-BTC exhibited enhanced adsorption capacity (839.7 mg·g−1) and high removal efficiency (99.8%) in the capture of uranium (VI) from aqueous solutions. Furthermore, the conditions such as adsorbent dose, contact time, and temperature in adsorption of uranium (VI) by RT-Cu-BTC were investigated in detail. The thermodynamics data demonstrated the spontaneous and endothermic nature of the uranium (VI) adsorption process. The Langmuir isotherm and pseudo-second-order models could better reflect the adsorption process of uranium (VI) onto RT-Cu-BTC. In addition, the as-synthesized RT-Cu-BTC showed excellent stability in removing uranium (VI) from an aqueous solution. This work provides a facile and rapid approach for fabricating hierarchically porous MOFs to realize a highly efficient removal of uranium (VI) from aqueous systems.