Convolutional neural networks are nowadays witnessing a major success in different pattern recognition problems. These learning models were basically designed to handle vectorial data such as images but their extension to non-vectorial and semi-structured data (namely graphs with variable sizes, topology, etc.) remains a major challenge, though a few interesting solutions are currently emerging.In this paper, we introduce MLGCN; a novel spectral Multi-Laplacian Graph Convolutional Network. The main contribution of this method resides in a new design principle that learns graph-laplacians as convex combinations of other elementary laplacians – each one dedicated to a particular topology of the input graphs. We also introduce a novel pooling operator, on graphs, that proceeds in two steps: context-dependent node expansion is achieved, followed by a global average pooling; the strength of this two-step process resides in its ability to preserve the discrimination power of nodes while achieving permutation invariance. Experiments conducted on SBU and UCF-101 datasets, show the validity of our method for the challenging task of action recognition.