Remaining useful life (RUL) prediction is an essential component for prognostics and health management of a system. Due to the powerful ability of nonlinear modeling, deep learning (DL) models have emerged as leading solutions by capturing temporal dependencies within time series sensory data. However, in RUL prediction tasks, data are typically collected from multiple sensors, introducing spatial dependencies in the form of sensor correlations. Existing methods are limited in effectively modeling and capturing the spatial dependencies, restricting their performance to learn representative features for RUL prediction. To overcome the limitations, we propose a novel LOcal-GlObal correlation fusion-based framework (LOGO). Our approach combines both local and global information to model sensor correlations effectively. From a local perspective, we account for local correlations that represent dynamic changes of sensor relationships in local ranges. Simultaneously, from a global perspective, we capture global correlations that depict relatively stable relations between sensors. An adaptive fusion mechanism is proposed to automatically fuse the correlations from different perspectives. Subsequently, we define sequential micrographs for each sample to effectively capture the fused correlations. Graph neural network (GNN) is introduced to capture the spatial dependencies within each micrograph, and the temporal dependencies between these sequential micrographs are then captured. This approach allows us to effectively model and capture the dependency information within the data for accurate RUL prediction. Extensive experiments have been conducted, verifying the effectiveness of our method.