Second-order long period wave forces acting on a two-dimensional fixed obstacle in bichromatic waves on the water of finite depth are investigated. Although the second-order diffraction problem has been solved by many researchers, only a few paper has been discussed the effect of second-order free waves generated by a wave maker. Therefore, in this paper, the second-order diffraction problem is solved exactly including the effects of second-order free waves generated by the wave maker, and the effect of it on the second-order diffraction potentials and wave forces are investigated. In this paper, for the theoretical simplicity, the second-order diffraction problem of a vertical flat plate in a two-dimensional water channel with paddle type wave maker is considerd, and the second-order long period wave forces calculated by exact method are compared to the results of more convenient method using Green's second identity and experimental results.