The objectives of the present paper are to develop a powerful numerical method for computing the second-order wave forces on a cone shaped floating structure and to clarify the nonlinear effects on the wave forces induced by the effects of the cross angles of body and water surface. In the present paper, the second-order wave exciting forces are obtained from the radiated wave potential of the double frequency and the first-order scattered wave potential by using the extended Haskind formula. The infinite integral over the free surface is evaluated by using the Fresnel and the Gaussian integrations and the effects of the cross angles of body and water surface is considered in the compuation. The numerical results for the second-order steady forces and the wave exciting forces are compared with the experimental results. The usefulness of the present method and the nonlinear effects are discussed.