This paper proposes a model predictive control (MPC) algorithm for Linear Parameter Varying (LPV) systems with unknown bounded delay, subject to input constraints. To deal with the delay, an optimization problem is formulated by applying the equivalence property. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) using relaxation matrices, satisfying the terminal inequality. The proposed MPC algorithm with the conditions guarantees the asymptotic stability of the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed method.