<p>This article proposes a new adaptive inductance estimator based on a full-order sliding mode virtual flux observer (FOSVFO), dedicating to improve the parameter robustness of predictive current control (PCC) strategy for grid-tied inverters (GTIs). First, the conventional FOSVFO-based inductance estimator is reviewed, revealing its drawbacks of sensitivity to grid frequency deviation and disability with zero active power. Second, to solve these problems, a complex-coefficient filter is creatively introduced to filter the grid voltage. Then, the filtered grid voltage and the observed virtual flux are utilized to design inductance estimator to counteract the effect of frequency deviation. Third, an inductance adaptive law is deduced by a newly designed Lyapunov function, which ensures the steady operation of the inductance estimator with zero active power, overcoming another drawback of the conventional inductance estimator. Finally, by substituting the estimated inductance into the PCC algorithm, the performance of the PCC for GTIs is improved significantly. Comparative experiments validate the effectiveness and superiority of the proposed techniques.</p>