Three-dimensional (3D) topological insulators are known for their strong spin-orbit coupling (SOC) and the existence of spin-textured surface states that might be potentially exploited for "topological spintronics." Here, we use spin pumping and the inverse spin Hall effect to demonstrate successful spin injection at room temperature from a metallic ferromagnet (CoFeB) into the prototypical 3D topological insulator Bi2Se3. The spin pumping process, driven by the magnetization dynamics of the metallic ferromagnet, introduces a spin current into the topological insulator layer, resulting in a broadening of the ferromagnetic resonance (FMR) line width. Theoretical modeling of spin pumping through the surface of Bi2Se3, as well as of the measured angular dependence of spin-charge conversion signal, suggests that pumped spin current is first greatly enhanced by the surface SOC and then converted into a dc-voltage signal primarily by the inverse spin Hall effect due to SOC of the bulk of Bi2Se3. We find that the FMR line width broadens significantly (more than a factor of 5) and we deduce a spin Hall angle as large as 0.43 in the Bi2Se3 layer.