This paper studies a long-standing problem of learning the representations of a whole graph without human supervision. The recent self-supervised learning methods train models to be invariant to the transformations (views) of the inputs. However, designing these views requires the experience of human experts. Inspired by adversarial training, we propose an adversarial self-supervised learning (\texttt{GASSL}) framework for learning unsupervised representations of graph data without any handcrafted views. \texttt{GASSL} automatically generates challenging views by adding perturbations to the input and are adversarially trained with respect to the encoder. Our method optimizes the min-max problem and utilizes a gradient accumulation strategy to accelerate the training process. Experimental on ten graph classification datasets show that the proposed approach is superior to state-of-the-art self-supervised learning baselines, which are competitive with supervised models.