When orthogonal frequency division multiplexing(OFDM) systems are applied to visible light communication(VLC), they are prone to issues such as multipath interference, frequency offset noise, and a high peak-to-average power ratio(PAPR). A filter bank multi-carrier (FBMC) based VLC system is proposed. Firstly, by employing offset quadrature amplitude modulation (OQAM) and a composite filter consisting of inverse fast fourier transform(IFFT) and polyphase network(PPN), the system effectively improves bit error rate performance and reduces out-of-band leakage. Then, it is validated through simulation using the Monte Carlo method. The simulation and experimental results show that under conditions where the number of subcarriers is 128, the modulation scheme is 16QAM, and the system bit error rate is 10^-3, the proposed system requires an improvement of approximately 5 dB in signal-to-noise ratio (SNR) compared to the OFDM system. Meanwhile, at a normalized frequency of 0.1, the out-of-band leakage power of the proposed system is reduced by 40 dB relative to the OFDM system, with the system's modulation error ratio(MER) reaching 19.6 dB.