Aiming at the problems of low positioning accuracy and high computational complexity of the traditional location fingerprint algorithm, this paper proposes a single Light Emitting Diode (LED) indoor positioning algorithm based on Back Propagation Neural Network and Multiple Linear Regression (MLR). First, three horizontal PhotoDetectors (PD) are used at the receiver side to receive optical power, and the point to be measured is located at the center of the receivers. Then, according to the received optical power vector, the BP neural network is used to obtain the coarse location range of the point to be measured. Finally, the location range is used as a constraint, and multiple linear regression is used to achieve more accurate positioning of the point. The experimental results demonstrate that in an indoor space of 2.0 m × 2.0 m × 2.5 m, the average positioning error of the algorithm is 5.04 cm, and the average positioning time is 0.002 83 s. Compared with the traditional location fingerprint algorithm, the average positioning accuracy of the algorithm is improved by 41.53%, and the average positioning time is reduced by 56.60%, which achieves more accurate positioning under the requirement of lower computational complexity.