Few-shot open-set recognition (FSOSR) aims to detect instances from unseen classes by utilizing a small set of labeled instances from closed-set classes. Accurately rejecting instances from open-set classes in the few-shot setting is fundamentally more challenging due to the weaker supervised signals resulting from fewer labels. Transformer-based few-shot methods exploit attention mapping to achieve a consistent representation. However, the softmax-generated attention map normalizes all the instances that assign unnecessary high attentive weights to those instances not close to the closed-set classes that negatively impact the detection performance. In addition, open-set samples that are similar to a certain closed-set class also pose a significant challenge to most existing FSOSR models. To address these challenges, we propose a novel Meta Evidential Transformer (MET) based FSOSR model that uses an evidential open-set loss to learn more compact closed-set class representations by effectively leveraging similar closed-set classes. MET further integrates an evidence-to-variance ratio to detect fundamentally challenging tasks and uses an evidence-guided cross-attention mechanism to better separate the difficult open-set samples. Experiments on real-world datasets demonstrate consistent improvement over existing competitive methods in unseen class recognition without deteriorating closed-set performance.