<p>Global Sensitivity Analysis (GSA) is a crucial step in uncertainty quantification, but it often requires significant computational costs to understand the relationship between the inputs and outputs. To address this issue, this paper proposes an adaptive updating GSA method based on multi-fidelity surrogate models (AHK-GSA). This method introduces a novel adaptive updating function based on high and low fidelity sensitivity analysis results. By maximizing this function, the accuracy of both surrogate model and sensitivity analysis can be simultaneously improved. Additionally, by computing the spatial distribution of sensitivity analysis errors during the iterative process, the method adaptively corrects the multi-fidelity surrogate model, achieving full integration of the surrogate model with sensitivity analysis. Four mathematical examples and a mechanics problem of metamaterial structures with negative Poisson ratio are used to verify the effectiveness of the proposed AHK-GSA. In mathematical examples, the proposed AHK-GSA method reduced computational cost in sensitivity analysis, with a maximum decrease of 47.1% in total cost. In mechanics problem of metamaterial structures with negative Poisson ratio, the proposed AHK-GSA method reduced computational costs by 23.3%, 39.5%, and 32.35% compared to the other three state-of-art methods.</p>