Remaining useful life (RUL) prediction plays a fundamental role in the prognostics and health management of mechanical equipment. Consequently, extensive research has been devoted to estimating the RUL of mechanical equipment. Owing to the development of modern advanced sensor technologies, a significant amount of monitoring data is recorded. Traditional methods, such as machine-learning-based methods and statistical-data-driven methods, are ineffective in matching when faced with big data thus leading to poor predictions. As a result, deep-learning-based methods are extensively utilized due to their efficient capability to excavate deep features and realize accurate predictions. However, most deep-learning-based methods only provide point estimations and ignore the prediction uncertainty. To address this limitation, this paper proposes a parallel prognostic network to sufficiently excavate the degradation features from multiple dimensions for more accurate RUL prediction. In addition, accurate calculation of model evidence is extremely difficult when dealing with big data so the Monte Carlo dropout is employed to infer the model weights under low computational cost and high scalability to obtain a probabilistic RUL prediction. Finally, the C-MAPSS aero-engine dataset is employed to validate the proposed dual-channel framework. The experimental results illustrate its superior prediction performance compared to other deep learning methods and the ability to quantify prediction uncertainty.