This paper presents an equivalent circuit of the hairpin line filter for accurate analysis and design. Its validity was verified by computer simulations and filter design experiments. Though the various design equations for a hairpin line filter have been proposed, there has not been a practically simplified equivalent circuit because it is hard to effectively represent interconnection effects between non-adjacent elements. In this paper, all the open ports of the hairpin line filter circuit are changed to the short ports using circuit duality, and the resulting circuits are transformed to graph model. The further simplified circuit model is obtained from boundary conditions, and then the final equivalent circuit of the hairpin line filter is derived in a dual structure of the filter.