The hypersonic missile control in the terminal phase is considered and addressed using higher order sliding mode control techniques. The third order sliding mode controller that comprises the continuous finite reaching time controller driven by the continuous higher order siding mode disturbance observers have been proposed, designed and studied. The proposed higher order sliding mode controller has been validated via simulations of a hypersonic missile in the terminal phase. The controllers demonstrated robustness and high accuracy of the output tracking in the presence of matched and unmatched external disturbances and missile model uncertainties.