Taking into account almost all kinds of variations and uncertainties to which AC island photovoltaic (PV) microgrid is often subjected, this paper proposes a new nonsingular fast terminal sliding mode control (NFTSMC) strategy for two-stage converters to enhance robustness against those disturbances and improve system dynamic performance. Firstly, to effectively decrease the adverse effect on the system from intermittent solar irradiation and uncertain environmental temperature, a NFTSMC cascaded with perturb and observe (P&O) scheme is put forward for fore-stage DC/DC converter, and PV output voltage is controlled to track its reference and thus maximum power point tracking (MPPT) performance is improved. Then, to significantly decrease the adverse effect on the system from variations of load and LC filter parameters, by incorporating an extended state observer (ESO) into NFTSMC, an ESO-based NFTSMC scheme is proposed for post-stage DC/AC converter, and the load voltage is regulated to track its reference and thus system robustness is strengthened, in which ESO is designed to replace load current sensor and thus reduce hardware cost. By using global terminal attractor without discontinuous switching function, the proposed NFTSMC strategy can not only strengthen system robustness but also improve system dynamic performance. Lastly, on account of the variations of PV generation and load demand, a conventional double-loop PI scheme is put into use for bidirectional DC/DC converter and thus system power balance is ensured. Comprehensive MATLAB simulation and StarSim/Hardware experiment results show that the proposed NFTSMC strategy for two-stage converters can overcome negative effects caused by various internal and external disturbances, and thus enable island PV microgrid to operate reliably and supply high-quality AC power.