We proposed a fingerprint matching and localization algorithm based on orthogonal frequency division multiplexing (OFDM) modulation for indoor visible light communication known as FMLA-OFDM. The experimental results show that compared with the traditional centroid localization algorithm, the average positioning accuracy of the proposed algorithm and the positioning stability are improved by 56% and 55%, respectively. Further, with the increase of the horizontal distance between LEDs, the positioning accuracy of the proposed algorithm is obviously superior to that of the positioning model based on the least square method. Finally, the average positioning accuracy and the positioning stability of the proposed algorithm are 17% and 21% higher than those of the positioning model based on the binary on-off keying (OOK) modulation mode, respectively.