This design of a linear parameter-varying (LPV)' controller for the rejection of sinusoidal disturbance with time-varying frequency but measurable on-line for implementation purposes is described. The approach proposed is based on modelling the sinusoidal disturbance with a measurable time-varying frequency as an LPV model and adding this model to the controlled linear time-invariant (LTJ) system to formulate an augmented LPV system. Then a stabilising H-like LPV controller is constructed for the augmented LPV system based on the Lyapunov approach with a single quadratic Lyapunov function. The effectiveness of the LPV controller is assessed by means of several simulation trials on a two-mass-spring-damper system. Numerical results are used to demonstrate the validity of the analytical results and the ability of the algorithms to reject sinusoidal disturbance with time-varying frequency.