Grid-forming inverters (GFMIs) suffer from inevitable performance degradation in the presence of parametric uncertainties when regulated by conventional model predictive control (MPC) in islanded operation. In this regard, a novel full-form dynamic linearization (FFDL)-based predictive control strategy is proposed to improve the voltage performance with enhanced parameter robustness for the islanded-mode GFMIs, which are purely data-driven and current sensorless. Specifically, the FFDL data model are introduced to identify the output voltage dynamic with-out requiring any prior knowledge of the precise mathematical model, while the cost function with multiple control targets is modified to avoid bringing extra system parameters. Therefore, the parameter sensitivity issue is effectively tackled since only the input/output data are utilized, enabling a strong robustness against the system parameter variations. Meanwhile, compared with the MPC method, the current information used to predict the output voltage is eliminated in the proposed scheme because both inductor and load currents are inherently excluded from the prediction model, which achieves current sensorless with enhanced system reliability. Moreover, to further lessen the computational burden, the cost function evaluation is simplified with only one voltage reference estimation by transforming the optimization process into a linear least square problem. Finally, comparative experimental results verify the effectiveness of the proposed strategy.