Wi-Fi indoor localization has witnessed an increasing interest, benefiting from its low cost, easy accessibility and wide deployment. However, its applications are often restricted due to harsh multipath propagation in indoor environments. In this letter, we propose a tensor-based localization algorithm that fully exploits the multipath components (MPCs) within the channel state information. We first formulate the location parameter estimation problem as a tensor decomposition problem and ensure the uniqueness by a preprocessing step. Then, a multipath-aided localization method is proposed to achieve high-accuracy localization via fusing time-difference-of-arrival and angle-of-arrival information from all MPCs. Experimental results show that the proposed method can provide a stable sub-meter-level localization performance in multipath environments.