Clinical event sequences consist of thousands of clinical events that represent records of patient care in time. Developing accurate prediction models for such sequences is of a great importance for defining representations of a patient state and for improving patient care. One important challenge of learning a good predictive model of clinical sequences is patient-specific variability. Based on underlying clinical complications, each patient's sequence may consist of different sets of clinical events. However, population-based models learned from such sequences may not accurately predict patient-specific dynamics of event sequences. To address the problem, we develop a new adaptive event sequence prediction framework that learns to adjust its prediction for individual patients through an online model update.