Graphs play a vital role in various applications. Graph Neural Networks (GNNs) excel at capturing topology information by using a message-passing mechanism to enrich node representations with local neighborhood information. Despite their success in modeling single-layer graphs, real-world scenarios often involve multi-layer graphs where nodes can have multiple edges or relationships represented as different layers. Existing methods of multi-layer graph learning struggle to efficiently process inter-layer information, as they mainly focus on preserving similar layers or shared invariant information, which may not be suitable for all situations. We propose a novel framework called Adaptive Multi-layer Graph Neural Networks (AmGNN) to address this challenge. AmGNN learns shared invariant information for nodes that need it and selectively preserves relevant layers’ information for nodes not requiring shared invariance. We introduce multi-layer graph contrastive learning to efficiently capture invariant information and learn weights for adaptive processing. Our experiments on real-world multi-layer graphs validate the effectiveness of AmGNN in node classification tasks.