A quantized vortex in the Bose-Einstein condensation (BEC), which is known to be unstable intrinsically, is demonstrated theoretically to be stabilized by the finite temperature effect. The mean-field calculation of Popov approximation within the Bogoliubov theory is employed, giving rise to a self-consistent solution for BEC confined by a harmonic potential. Physical origin of this vortex stabilization is investigated. An equivalent effect is also proved to be induced by an additional pinning potential at the vortex center produced by a focused laser beam even at the lowest temperature. The self-consistent solutions give detailed properties of a stable vortex, such as the spatial profiles of the condensate and non-condensate, the particle current density around the core, the whole excitation spectrum, and their temperature dependences.