Quantization has been widely employed in analog-to-digital conversion (ADC) for the acquisition of digital data, which are further utilized for prognostics. However, quantization errors are inevitable during ADC, resulting in bias in the subsequent prognosis results. Compared to the numerous researches on prognosis considering measurement noises, slight attention has been paid on remaining useful life (RUL) for degrading devices incorporating quantization errors. In this study, a Wiener-process-based model incorporating mixed random noise is utilized to describe the degradation process involving quantization errors. In order to mitigate the impact of quantization errors, a parameter identification approach and a degradation state estimation method are proposed, which integrate maximum likelihood estimation, particle filter, and Bayesian inference. Subsequently, the results of RUL prediction with and without considering quantization errors are derived, respectively. Finally, numerical examples and a case study on the degradation data from control moment gyroscopes (CMG) are provided to demonstrate the proposed method.