Multi-label text classification (MLTC) faces significant challenges in real-world scenarios due to complex label correlations and the scarcity of labeled data. Existing MLTC methods typically rely on large amounts of labeled data to learn text representations and label dependencies, severely limiting their few-shot ability. While prompt tuning has recently emerged as an effective few-shot learning strategy, its potential in MLTC remains underexplored due to the inherent gap between masked language modeling and multi-label classification. In this paper, we propose a Dual-Verbalizer framework with Label Correlation modeling (DVLC)(The code is available at: https://anonymous.4open.science/r/DVLC ) for few-shot MLTC, integrating multi-label correlation modeling into the prompt tuning framework. Specifically, we introduce text-specific continuous prefixes that incorporate text features into soft prompts, and develop a GCN-based verbalizer with multi-label modeling, which collaborates with a mask verbalizer for prediction. In addition, we apply supervised contrastive learning based on multi-label similarity to improve generalization and mitigate overfitting. Extensive experiments demonstrate the effectiveness of DVLC in few-shot settings.