A cam phase control apparatus for an internal combustion engine is provided for improving the controllability in a transient state in which an actual cam phase converges to a target cam phase to accurately and readily identify model parameters even when a mechanism for changing the actual cam phase exhibits an intense friction characteristic. The cam phase control apparatus relies on a sliding mode control algorithm which models a controlled object that receives the control input to a cam phase varying device and outputs an actual cam phase as a discrete time based model, and creates a switching function as a function of time series data of a following error. An ECU functions as a sliding mode controller for determining the control input to the cam phase varying device at a predetermined control period for converging the actual cam phase to a target cam phase.