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Online monitoring aims to evaluate or to predict, at runtime, whether or not the behaviors of a system satisfy some desired specification. It plays a key role in safety-critical cyber-physical systems. In this work, we propose a new monitoring approach, called model predictive monitoring, for specifications described by Signal Temporal Logic (STL) formulae. Specifically, we assume that the observed state traces are generated by an underlying dynamical system whose model is known but the control law is unknown. The main idea is to use the dynamic of the system to predict future states when evaluating the satisfaction of the STL formulae. To this end, effective approaches for the computation of feasible sets of STL formulae are provided. We show that, by explicitly utilizing the model information of the dynamical system, the proposed online monitoring algorithm can falsify or certify of the specification in advance compared with existing algorithms, where no model information is used. We also demonstrate the proposed monitoring algorithm by several real world case studies.