In multi-user downlink indoor visible light communication system based on non-orthogonal multiple access technology (VLC-NOMA), an iterative power allocation scheme based on weighted sum-rate maximization was proposed to solve the problem of the conflict between sum-rate and user fairness. The objective of this scheme is to maximize the weighted sum-rate, and the user fairness can be adjusted by changing the weighted factor. Since the target problem is a non-convex optimization problem, this non-convex problem is transformed into a concave problem by auxiliary variable method and convex optimization theory, then solved by the Lagrange dual method, and an iterative power allocation algorithm is designed according to the solution of the problem. The convergence of the proposed algorithm, system sum-rate and user fairness are simulated. Results show that the proposed iterative power allocation algorithm has good convergence, VLC-NOMA system can obtain better sum-rate performance than VLC-OMA system. By adjusting the weighted factor, better system sum-rate and user fairness can be obtained than the existing power allocation scheme at the smaller expense of system sum-rate.