For highly reliable and long-life products, accelerated degradation test (ADT) is often an effective and attractive way to assess the reliability. To analyze the accelerated degradation data, it has been well recognized that it is necessary to incorporate three sources of variability including the temporal variability, the unit-to-unit variability and measurement errors into the ADT model. The temporal variability can be properly described by the Wiener process. However, the randomness of the initial degradation level, which is an important part of the unit-to-unit variability, has been often neglected. In addition, regarding the measurement errors, current ADT models often assumed them to follow a mutually independent normal distribution and ignored the autocorrelation that may probably exist in them. These problems lead to a poor accuracy for reliability evaluation in some situation. Thus, a random-effect Wiener process-based ADT model considering one-order autoregressive (AR(1)) errors is proposed. Then closed-form expressions for the failure time distribution (FTD) is derived based on the concept of first hitting time (FHT). A statistical inference method is adopted to estimate unknown parameters. Finally, a comprehensive simulation study and a practical application are given to demonstrate the rationality and effectiveness of the proposed model