With the continuous progress of science and technology, people have put forward higher requirements for indoor positioning services. For the problems of low positioning accuracy, complex and expensive equipment of traditional indoor positioning technology, a multi-light-emitting diode (LED) indoor positioning method based on extreme learning machine (ELM) neural network is proposed in this paper. First, the optical power of LEDs at each reference point and the position coordinates of the photodetector are used as fingerprint data to construct a fingerprint database. Then, the fingerprint database is introduced into the ELM neural network model for training, and the light intensity-based localization model is established. The simulation results show that the time for training the data set of the method is only 0.0687 s in a localization area of 4 m×4 m×3 m, and the average localization accuracy can reach 1.17 cm.