Class-incremental learning (CIL) enables models to learn new classes continually without forgetting previously acquired knowledge. Multi-label CIL (MLCIL) extends CIL to a real-world scenario where each sample may belong to multiple classes, introducing several challenges: label absence, which leads to incomplete historical information due to missing labels, and class imbalance, which results in the model bias toward majority classes. To address these challenges, we propose Label-Augmented Analytic Adaptation (L3A), an exemplar-free approach without storing past samples. L3A integrates two key modules. The pseudo-label (PL) module implements label augmentation by generating pseudo-labels for current phase samples, addressing the label absence problem. The weighted analytic classifier (WAC) derives a closed-form solution for neural networks. It introduces sample-specific weights to adaptively balance the class contribution and mitigate class imbalance. Experiments on MS-COCO and PASCAL VOC datasets demonstrate that L3A outperforms existing methods in MLCIL tasks. Our code is available at https://github.com/scut-zx/L3A.