Recently, learning open-vocabulary semantic segmentation from text supervision has achieved promising downstream performance. Nevertheless, current approaches encounter an alignment granularity gap owing to the absence of dense annotations, wherein they learn coarse image/region-text alignment during training yet perform group/pixel-level predictions at inference. Such discrepancy leads to suboptimal learning efficiency and inferior zero-shot segmentation results. In this paper, we introduce a Multi-Grained Cross-modal Alignment (MGCA) framework, which explicitly learns pixel-level alignment along with object- and region-level alignment to bridge the granularity gap without any dense annotations. Specifically, MGCA ingeniously constructs pseudo multi-granular semantic correspondences upon image-text pairs and collaborates with hard sampling strategies to facilitate fine-grained cross-modal contrastive learning. Further, we point out the defects of existing group and pixel prediction units in downstream segmentation and develop an adaptive semantic unit which effectively mitigates their dilemmas including under- and over-segmentation. Training solely on CC3M, our method achieves significant advancements over state-of-the-art methods, demonstrating its effectiveness and efficiency.