This work is devoted to design of interval observers for a class of Linear-Parameter-Varying (LPV) systems. Applying High Order Sliding Mode (HOSM) techniques it is possible to decrease the initial level of uncertainty in the system, which leads to improvement of set-membership estimates generated by an interval observer. In addition, it is shown that HOSM techniques may relax the applicability conditions of the interval observer design methods. The efficiency of the proposed approach is demonstrated through computer simulations.