Remaining Useful Life （RUL） prediction is the key technique to implement the health management of stochastic degrading equipment. As one of the typical methods for RUL prediction， statistical data-driven methods generally adopt the stochastic model to characterize the evolving progression of the equipment performance degradation variable and provide the probabilistic distribution of the RUL to facilitate the uncertainty quantification of the RUL prediction. However， selecting the functional form of the degradation model is itself a challenging problem. More importantly， inappropriate selection of the functional form for the degradation model leads to difficult and ineffective calibration of the degradation model simply by updating the model parameters， thus affecting prediction accuracy. In this paper， an equipment RUL prediction method is developed based on the dynamic calibration of degradation models. First， a stochastic degradation model is constructed based on the nonlinear diffusion process and the model parameters are estimated through the degradation monitoring data of the equipment to predict the future degradation trend. Then， a parametric model for the degradation prediction errors is established to compensate for the degradation model to calibrate its functional form. Meanwhile， the calibrated model parameters are updated based on the Bayesian method to achieve simultaneous calibration of the functional form and the degradation model parameters. With the calibrated model， the equipment RUL distribution is derived for the RUL prediction. Finally， the developed method is validated by numerical simulations and lithium battery data.