Spectral variability remains a major challenge in hyperspectral unmixing, as the spectral signatures of the same material often fluctuate under different illumination, atmospheric, or scale conditions, which invalidates the fixed endmember assumption. To address this issue, we propose Meta-Spectral Net, a meta-learning-based framework for adaptive spectral variability modeling in hyperspectral unmixing. The proposed framework leverages a task-driven meta-learning strategy, where each acquisition scenario is defined as a task, to enable the endmember generator to rapidly adapt to unseen spectral conditions with only a few samples. Furthermore, a spectral variability adaptation module is introduced to explicitly account for environmental factors, thus improving the robustness of endmember representation. Comprehensive experiments on both synthetic and real hyperspectral datasets demonstrate that Meta-Spectral Net significantly outperforms state-of-the-art unmixing methods in terms of endmember reconstruction accuracy and abundance estimation, while offering superior generalization to novel scenarios. These results suggest that meta-learning provides an effective paradigm for tackling spectral variability, paving the way toward more adaptive and reliable hyperspectral unmixing in real-world applications.