Recurrent processes can occur in multiple locations that form a network. The occurrence of recurrent events can be affected by event occurrences at other locations and covariates such as event durations. In such scenario, the dependent structure among the occurrence of recurrent events at different locations is of interest, as well as the prediction of future events given the event and covariate history. Motivated by a prediction application of geyser eruption, we develop a covariate-adjusted recurrent process (CARP) model. The model uses conditional multivariate normal distribution to describe the time to events from different locations, and the correlation structure is captured by the variance-covariance matrix. We also incorporate covariate information into the mean structure. We use maximum likelihood method to estimate the model parameters. Simulations are used to study the property of the developed procedure. We finally illustrate the developed method by using Yellowstone geyser eruption data.