Faster-than-Nyquist technology can significantly improve the transmission rate of wireless optical communication system, but the atmospheric turbulence seriously affects the performance of faster-than-Nyquist wireless optical communication (FTN-OWC) system. In this paper, the influence of light intensity fading in exponential Weibull turbulent channel on the ergodic capacity and outage capacity of the FTN-OWC system is studied in detail. Based on pulse amplitude modulation, the ergodic capacity upper bound and outage probability of the FTN-OWC system are derived, and its closed-form expression is obtained by using the generalized hypergeometric method. In addition, the impact of acceleration factor, roll-off coefficient, turbulence intensity, and receiving aperture on the ergodic capacity and outage capacity is discussed. The results show that the ergodic capacity and outage capacity are reduced when the turbulence increases, but they can be improved by increasing the receiving aperture and roll-off coefficient. In the case of weak turbulence, the ergodic capacity of the FTN-OWC system is improved by 16.43% compared to the Nyquist wireless optical communication system using the same modulation method when the receiving aperture is 25 mm, the roll-off coefficient is 0.5, the acceleration factor is 2/3, and the average signal to noise ratio is 30 dB.