It is known that a ship can be regarded as a type of wave measuring device, and under the assumption of linear superposition, wave spectra can thus be estimated from measured spectra of ship motions. Based on this idea, the evaluation of one-dimensional wave spectra, as well as directional wave spectra, has been extensively carried out in recent years. However, when a ship is traveling with an advance speed in following seas, there is a range of encounter frequencies ω _e for which cannot be related to the wave frequencies ω by a single-value conversion. Practically, this difficulty has been solved by keeping the lowest frequency solution, however resulting spectra may only a narrow range of wave frequency when a ship navigates with high speed in following seas. In the previous paper, we proposed to determine the wave spectrum by using a nonlinear programming method, in which a standard wave spectrum, such as the ISSC, is selected, and a significant wave height and average wave period are used as design variables. The optimization was carried out in the wave frequency domain. In this paper, we propose to determine the wave spectrum by using a method in which the ordinates of wave spectrum at an arbitrary wave frequency are used as design variables and the optimization has been carried out in the encounter frequency of the ship. The capability of this approach has been confirmed by comparing the wave spectra estimated from the measured motions of container and ore-carrier models, with the ones obtained from the direct measurement of waves in the experimental tank.