This paper proposes a visible light fingerprint positioning scheme based on a convolutional neural network (CNN) to improve the performance of indoor visible light positioning systems. In the proposed scheme, optical intensity signals are employed as the features of the reference node LED, and receiver coordinates are employed as training labels to construct fingerprint database. In addition, a positioning model based on light intensity information is constructed, and a one-dimensional CNN learning model is adopted for training. CNN application solves the problems of low-positioning accuracy and poor stability of the fully-connected feedforward neural network method. In an indoor-positioning scene (size: 5 m×5 m×3 m), the proposed positioning scheme obtained high positioning accuracy with an average positioning error of 4.44 cm. In addition, the performance of several different indoor visible light positioning methods was compared and analyzed in simulation experiments, and the results verified the technical advantages of the proposed scheme.