Bayesian modelling procedure is applied to an inverse problem of how to estimate directional wave spectra from actual ship motion data. The data were recorded by the Voyage Data Recorder equipped on a real container carrier which was put on the North Pacific Line. As for the ordinary merchant ships, it is very difficult to know the actual parameters of rolling motion, such as natural periods, dumping coefficients and metacentric heights GM. And, it is almost impossible to get the hull form offset data which is required for the accurate calculation of the ship motion response functions. Therefore, it is the main purpose of this paper to clarify the availability of the Bayesian modelling procedure to the inverse problem under the unreliable conditions. Compared with the wave direction measured by visual observations, it has shown that the estimated directional wave spectra have some peaks in the observed wave direction. This concludes that the Bayesian modelling procedure is a powerful tool for estimating the wave direction.