Point process is an expressive tool in learning temporal event sequence which is ubiquitous in real-world applications. Traditional predictive models are based on maximum likelihood estimation (MLE). This paper aims to improve MLE by discriminative and adversarial learning. The initial model is learned by MLE explaining the joint distribution of the occurred event history. Then it is refined by devising a gradient based learning procedure with two complementary recipes: i) mean square error (MSE) that directly reflects the prediction accuracy of the model; ii) adversarial classification loss which induces the Wasserstein distance loss. The hope is that the adversarial loss can add sharpness to the smooth effect inherently caused by the MSE loss. The method is generic and compatible with different differentiable parametric forms of the intensity function. Empirical results via a variant of the Hawkes processes demonstrate its effectiveness of our method.