Indoor light-emitting diode (LED) light sources are with non-flat light intensity distribution, and the conventional Lambert model fails to take indirect channels, noise and interference in the environment, obstruction, interior borders, and irregular room layouts into account. To address these problems, this paper proposes an optimal light source layout scheme based on a parallel fully connected convolutional neural network (PFCNN) model for indoor visible light positioning (VLP). The datasets in the fingerprint database are constructed by collecting light source information, such as the coordinates, power, and orientation angle of the light source, and the corresponding light intensity distribution on the receiving plane. The parameter characterizing the flatness of light intensity distribution is measured by a Monte Carlo method, and a fully connected neural network and a parallel fully connected neural network are utilized to build a visible light channel model. A prediction model for light intensity flatness is then developed by the proposed PFCNN model, and an optimal light source layout is achieved by the momentum particle swarm optimization K-Means++ (Mot-PSO-K-Means++) algorithm. Simulation analysis shows that parallel fully connected neural networks improve accuracy by 84.69% compared with that of fully connected neural networks. In the 5 m×5 m×3 m indoor space, light intensity flatness reaches 92.00% under the 4-LED layout, and light intensity ranges from 340 lx to 440 lx. Those under the 12-LED layout are, respectively, 92.00% and 980-1120 lx. Therefore, the proposed scheme, with higher flatness and applicability, can be applied to actual indoor VLP scenes, and it can provide theoretical support for in-depth research of indoor VLP.