In the existing studies, the Markov process model without memory effects is usually used to describe the random degradation of optoelectronic equipment, ignoring the long-term correlation of states in the degradation process. In view of this, we firstly proposed a random degradation model with memory effects based on nonlinear fractional Brownian motion to describe the degradation process of optoelectronic equipment under the influence of measurement errors and random effects. On this basis, we employed the weak convergence theory to derive the approximate analytical formula of the remaining useful life of equipment in the sense of the first hitting time. Secondly, we adopted the maximum likelihood estimation algorithm and Bayesian inference to complete the offline estimation and real-time update of the model parameters, thus realizing the adaptive prediction of the remaining useful life. Finally, the proposed method was applied to the performance monitoring data of GaAs lasers. The experimental results show that the proposed method can effectively improve the prediction accuracy of the remaining useful life of optoelectronic equipment.