The number of N‑k contingency combinations is enormous, and existing data‑driven transient stability contingency screening methods require large amounts of training data, resulting in high computational costs. To address this issue, a few‑shot N‑k transient stability screening method based on meta‑learning and an improved Transformer is proposed. Fault feature matrices are constructed using pre‑ and post‑fault electrical quantities to form N‑k meta‑learning tasks with low‑order faults as the support set and high‑order faults as the query set. A Transformer‑based meta‑learning algorithm for combined failures (T‑MLCF) fusing a relation network and a contrastive network is proposed to learn the nonlinear similarity and combinatorial knowledge. Case studies on the IEEE 39‑bus system demonstrate that T‑MLCF achieves superior few‑shot learning, generalization, and robustness, significantly reducing simulation costs.