Due to the facts that the degradation of inertial device is nonlinear and the historical degradation data is limited, a nonlinear degradation process model is utilized to estimate the Remaining Useful Life (RUL) of inertial device, and a Bayes method suitable for nonlinear degradation process is proposed. At first, non-informative prior distribution of two parameters is obtained by using Fisher information matrix. Then, by using likelihood function of independent increment, it is found that the parameters follow Gaussian-Inverse Gamma distribution. The first posterior distribution is obtained by using compatible historical degradation data and the second posterior distribution is obtained by using new degradation data. The parameters of single device and results of RUL are real-time updated in the end. The experiments show that the assessment result of nonlinear degradation process model is more accurate than the Wiener model. The RUL real-time prediction is achieved by utilizing the Bayes method, which can provide a reference for maintaining the inertial device.