Multimodal Sentiment Analysis (MSA) aims to recognize human emotions by exploiting textual, acoustic, and visual modalities, and thus how to make full use of the interactions between different modalities is a central challenge of MSA. Interaction contains alignment and conflict aspects. Current works mainly emphasize alignment and the inherent differences between unimodal modalities, neglecting the fact that there are also potential conflicts between bimodal combinations. Additionally, multi-task learning-based conflict modeling methods often rely on the unstable generated labels. To address these challenges, we propose a novel multi-level conflict-aware network (MCAN) for multimodal sentiment analysis, which progressively segregates alignment and conflict constituents from unimodal and bimodal representations, and further exploits the conflict constituents with the conflict modeling branch. In the conflict modeling branch, we conduct discrepancy constraints at both the representation and predicted output levels, avoiding dependence on the generated labels. Experimental results on the CMU-MOSI and CMU-MOSEI datasets demonstrate the effectiveness of the proposed MCAN.