Nonlinearity and implicitness are common degradation features of the stochastic degradation equipment for prognostics. These features have an uncertain effect on the remaining useful life (RUL) prediction of the equipment. The current data-driven RUL prediction method has not systematically studied the nonlinear hid-den degradation modeling and the RUL distribution function. This paper uses the nonlinear Wiener process to build a dual nonlinear implicit degradation model. Based on the historical measured data of similar equipment, the maximum likelihood estimation algorithm is used to estimate the fixed coefficients and the prior distribution of a random coefficient. Using the on-site measured data of the target equipment, the posterior distribution of a random coefficient and actual degradation state are step-by-step updated based on Bayesian inference and the extended Kalman filtering algorithm. The analytical form of the RUL distribution function is derived based on the first hitting time distribution. Combined with the two case studies, the proposed method is verified to have certain ad-vantages over the existing methods in the accuracy of prediction.