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The longitudinal motion model of a winged-cone configuration near space hypersonic flight vehicle is presented. Then the constituted nonlinear motion equations are linearized under different flight height and velocity to form a series of linear systems by small disturbance method. Each linear model is considered as a mode of a Markov jump system, which in whole make up a Markov jump system for the control of the longitudinal motion of the mentioned hypersonic flight vehicle. A state feedback robust variance controller which guarantees the closed-loop steady-state variance to be less than a given upper bound and possesses some H∞ performance is developed for the Markov jump linear system with white noise and uncertainties. Based on LMI method, conditions of existence of such controllers are proposed and proved. A parameterized representation of the desired controller is characterized in terms of the feasible solutions to a set of linear matrix inequations.