This paper proposed a design method for delay-dependent robust H-infinity filter of linear systems with uncertainty and time-varying interval delay. The proposed method was shown to be much simpler than existing ones while giving significant improvement to the existing results. The key step in the method was to construct a special type of Lyapunov functional for the filter design problem. Unlike the existing techniques, the proposed method employed neither free weighting matrices nor any model transformation, leading to reduced computational demand as well as improved performance. Numerical examples were given to demonstrate the effectiveness of the proposed method.