Contrastive learning, as a self-supervised learning paradigm, becomes popular for Multivariate Time-Series (MTS) classification. It ensures the consistency across different views of unlabeled samples and then learns effective representations for these samples. Existing contrastive learning methods mainly focus on achieving temporal consistency with temporal augmentation and contrasting techniques, aiming to preserve temporal patterns against perturbations for MTS data. However, they overlook spatial consistency that requires the stability of individual sensors and their correlations. As MTS data typically originate from multiple sensors, ensuring spatial consistency becomes essential for the overall performance of contrastive learning on MTS data. Thus, we propose Graph Contextual Contrasting (GCC) for spatial consistency across MTS data. Specifically, we propose graph augmentations including node and edge augmentations to preserve the stability of sensors and their correlations, followed by graph contrasting with both node- and graph-level contrasting to extract robust sensor- and global-level features. We further introduce multi-window temporal contrasting to ensure temporal consistency in the data for each sensor. Extensive experiments demonstrate that our proposed GCC achieves state-of-the-art performance on various MTS classification tasks.