In the recent method of analysis for the ship's motions in a seaway, the spectrum analysis of the measured records of motions has been used as an effective expression for the ship's characteristic response to the waves. In this analysis, the spectrum is calculated by Fourier transformation from the correlogram on the measured records of the motions. In this paper, the author applied the auto-regressive analysis for the study of the ship's motion induced by ocean waves and discussed it. At first, as the ship's motion in a seaway is a stationary stochastic process, the mathematical expressions of the motions are described and the data processing method for the measured ship's motions records are explained. The author examined the statistical properties of the motions on the data from equally spaced time interval reading of the records of motions. It was found that the distributions of data were Gaussian, and the characteristic response of the ship's motions for waves could be considered as the linear system, statistically, by the use of the cross spectrum analysis of the motions and waves. Then, the spectra for motions were calculated by the use of auto-regressive models and shown in Fig. 3-2, Fig. 3-4A and 3-4B. These models were determined by the use of equations (3-2) and (3-3). From these results it can be confirmed that the spectrum from an auto-regressive model is the more effective expression of the ship's motion and available in the problem of predictions of the ship's motions in a seaway.