It is well known that 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 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 of the ship, which cannot be related to the wave frequency by a single-value transformation. In the previous paper, we proposed a method to overcome this difficulty, and evaluated one-dimensional wave spectrum by using nonlinear programming. In this paper, we extend the method used for the estimation of one-dimensional wave spectrum to evaluate the directional wave spectrum. The capability of this approach has been discussed by comparing the estimated average wave periods and significant wave heights with those evaluated from the so-called SMB Method and the observation data written in logbook.