The problem of H-infinity filter design for linear systems with interval time-varying delay is investigated. The interval time-varying delay is considered as two cases: continuous and differentiable with the bounded derivative of the time-varying delay. Neither model transformation nor bounding techniques for cross terms is employed. A delay-dependent sufficient condition on the existence of an H-infinity filter is derived in the form of non-convex matrix inequalities by introducing a new Lyapunov Krasovskii functional which is based on both left and right endpoints of the time-varying delay interval. In order to find a feasible solution to the non-convex matrix inequalities, a minimisation problem is formulated and the problem can be solved by using a cone complementarity. Finally, two examples are given to illustrate the effectiveness of the proposed method.