For the nonlinear degradation equipment which widely exists in practice, the current RUL (remaining useful lifetime) prediction methods ignore the effect of random failure threshold. Therefore, the RUL prediction method based on nonlinear degradation processes with random failure threshold was proposed by analyzing equipment′s degradation processes. A nonlinear degradation model based on Wiener process with the individual difference and measurement error was built in this work. Next, the degradation states were updated synchronously by applying the Kalman filtering algorithm and constructing the state-space model. And then, the estimation method of failure threshold distribution parameters based on maximum likelihood estimation was proposed to obtain the probability distribution of the random failure threshold. Finally, an analytical and closed-form RUL distribution based on random failure threshold was derived, and the RUL prediction can be adaptively updated with the available observed data. The case study shows that the presented method can significantly improve the accuracy of RUL prediction and thus it has a certain engineering application value.