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Ubiquitous light-emitting diodes provide natural infrastructures for multiuser visible light communications (VLCs). However, the current available works for multiuser VLC systems mainly focus on broadcast scenarios and beamforming techniques. In this paper, we consider a multiuser multi-access VLC system with finite-alphabet inputs. Intended for two-user multi-access VLC systems, we propose an energy-efficient time-collaborative constellation design to manage the nonnegative multiuser interference and we develop a joint maximum-likelihood demodulation and successive interference cancellation decoding algorithm for signal detection. Simulation results indicate that our proposed time-collaborative constellation design outperforms time-uncollaborative scheme in error performance perspective.