Real-world event sequences consist of complex mixtures of different types of events occurring in time. An event may depend on past events of the same type, as well as, the other types. Point processes define a general class of models for event sequences. ``Regressive point processes'' refer to point processes that directly model the dependency between an event and any past event, an example of which is a Hawkes process. In this work, we propose and develop a new nonparametric regressive point process model based on Gaussian processes. We show that our model can represent better many commonly observed real-world event sequences and capture the dependencies between events that are difficult to model using existing nonparametric Hawkes process variants. We demonstrate the improved predictive performance of our model against state-of-the-art baselines on multiple synthetic and real-world datasets.