This paper is concerned with the H ∞ control problem for a class of linear parameter-varying (LPV) systems with randomly multi-step sensor delays. A mathematical model which describes the randomly multi-step sensor delayed measurements for LPV systems is established. An improved Lyapunov functional is proposed to determine the asymptotically mean-square stability of the closed-loop system which depends on the varying parameters. The obtained full-order parameter-dependent dynamic feedback controller guarantees the considered system to be asymptotically mean-square stable and to satisfy the modified H ∞ performance for all possible delayed measurements. An extended cone complementarity linearization method (CCLM) is used to solve the constrained linear matrix inequality (CLMI). Simulation results illustrate the effectiveness of the proposed method.