In recent years, indoor localization algorithms have attracted a great deal of attention and research interest. For the improvement of the complexity as well as the accuracy of existing localization algorithms, this paper proposes a visible light indoor localization algorithm that first uses Elman neural networks for indoor localization prediction and then uses the weighted K-nearest neighbor (WKNN) algorithm to correct the prediction results. The algorithm is applied in an indoor localization system with a single LED as a transmitter and four horizontal photoelectric detectors (PDs) as receivers. The four horizontal PDs are located at the four corners of the receiver and the position to be measured is located at the center of the receiver. The initial position of the point to be measured is first determined by predicting the horizontal and vertical coordinates of the point by two Elman neural networks. Then the point to be measured with a positioning error greater than the average error predicted by the neural network prediction is identified and corrected with the WKNN algorithm to determine the exact position of the point to be measured, and the corrected position is updated into the overall position of the point to be measured. The simulation results show that the average positioning error of this algorithm is 7.13 cm and the average positioning time is 0.24 s in an indoor environment of 3.6 m×3.6 m×3 m.