The corrosion evolution of oil and gas transmission pipelines is highly complicated, and sufficient data on influencing factors are often difficult to obtain in actual operation. Additionally, traditional empirical models produce significant errors in long-term predictions. To more comprehensively characterize the dynamic characteristics associated with memory effects and measurement randomness in pipeline corrosion, this paper proposes a non-Markov Wiener process prediction model considering both measurement errors and historical dependency. Model parameters are estimated and updated using maximum likelihood estimation and Bayesian inference. Based on weak convergence theory and the definition of first-passage failure time, an approximate analytical solution for the distribution of corrosion depth is derived, enabling predictive assessment of internal corrosion progression. Finally, monitoring data from the inner wall of a natural gas pipeline in the Chongqing Gas Mine are used to verify the effectiveness of the proposed method.