In this paper, a low-complexity, sparsity adaptive compressed sensing algorithm is proposed based on fingerprint localization of visible light communication. First, the localization problem is transformed into a sparse matrix reconstruction problem based on the sparsity of location fingerprints. Second, the nearest neighbor value is adaptively calculated based on the reconstructed residual value. Finally, the impact of fingerprint sampling interval, signal-to-noise ratio, modulation bandwidth, and transmission power on positioning errors are analyzed in detail. Moreover, the time complexity, distribution of the optimal nearest neighbor values, number of the light-emitting diodes, and maximum number of nearest neighbor fingerprints of the proposed positioning algorithm on positioning errors are also analyzed. The simulation results show that the proposed positioning algorithm has comparatively low average calculation time and small positioning error. When the signal-to-noise ratio and the distance between the fingerprints are 10 dB and 40 cm, respectively, the average positioning error of the proposed positioning algorithm is 1.56 cm, which is significantly lower than those of existing algorithms.