We detected the spin polarization due to charge flow in the spin nondegenerate surface state of a three-dimensional topological insulator by means of an all-electrical method. The charge current in the bulk-insulating topological insulator Bi1.5Sb0.5Te1.7Se1.3 (BSTS) was injected/extracted through a ferromagnetic electrode made of Ni80Fe20, and an unusual current-direction-dependent magnetoresistance gave evidence for the appearance of spin polarization, which leads to a spin-dependent resistance at the BSTS/Ni80Fe20 interface. In contrast, our control experiment on Bi2Se3 gave null result. These observations demonstrate the importance of the Fermi-level control for the electrical detection of the spin polarization in topological insulators.