The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. An interval predictor/observer is also proposed with improved accuracy for the case when an information is available about the frequency spectrum of the input signals. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.