We address the problem of abnormal event detection from trajectory data. In this paper, a new adversarial approach is proposed for building a deep neural network binary classifier, trained in an unsupervised fashion, that can distinguish normal from abnormal trajectory-based events without the need for setting manual detection threshold. Inspired by the generative adversarial network (GAN) framework, our GAN version is a discriminative one in which the discriminator is trained to distinguish normal and abnormal trajectory reconstruction errors given by a deep autoencoder. With urban traffic videos and their associated trajectories, our proposed method gives the best accuracy for abnormal trajectory detection. In addition, our model can easily be generalized for abnormal trajectory-based event detection and can still yield the best behavioural detection results as demonstrated on the CAVIAR dataset.