We propose a novel and trainable graph unpooling layer for effective graph generation. Given a graph with features, the unpooling layer enlarges this graph and learns its desired new structure and features. Since this unpooling layer is trainable, it can be applied to graph generation either in the decoder of a variational autoencoder or in the generator of a generative adversarial network (GAN). We guarantee that the unpooled graph remains connected and any connected graph can be sequentially unpooled from a 3-nodes graph. We apply the unpooling layer within the GAN generator and address the specific task of molecular generation. Using the QM9 and ZINC datasets, we demonstrate competitive performance of our method in comparison to other state-of-the-art approaches. This is a joint work with Yinglong Guo and Dongmian Zou