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For the uncertain linear systems described by the linear parameter varying (LPV) model, a parameter-dependent open-loop model predictive control (MPC) is proposed. The controller applies a tree trajectory to generate the vertices of uncertainty state predictions. Based on the state prediction tree, the future free control moves are parameter-dependent, whose vertices correspond to those of state predictions. The cost function penalizes the deviations of all the vertices of state/input from their steady-state target values. It is shown that the offset-free property is achieved by this method. A simulation example is given to demonstrate effectiveness of the approach.