Needless to say, the accumulation of a reliable database of ocean wave characteristics is very important for safe ship design and navigation. Usually, such information has been collected from reports based on shipboard visual observations. On the other hand, a ship can be regarded as a type of wave recorder and, under the assumption of linear superposition, wave spectra can thus be estimated from measured 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 the encounter frequency ω _e of the ship for which ω _e cannot be related to the wave frequency by a single-value transformation. Practically, this difficulty has been addressed by using an approximate method where only one solution ω of the relationship is retained by partitioning the ω-axis. When one keeps the lowest-frequency ω solution, however, resulting spectra tend to be narrower and displaced towards low frequencies. In this study, we propose to design a 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 parameters. The capability of this approach has been confirmed by comparing its results, based on the full-scale measurements of the motions of a container ship, with those from the so-called SMB method.