Weakly-Supervised Semantic Segmentation (WSSS) aims to train segmentation models using training image data with only image-level supervision. Since precise pixel-level annotations are not accessible, existing methods typically focus on producing pseudo masks for training segmentation models by refining CAM-like heatmaps. However, the produced heatmaps may only capture discriminative image regions of target object categories or the associated co-occurring backgrounds. To address the issues, we propose a Semantic Prompt Learning for WSSS (SemPLeS) framework, which learns to effectively prompt the CLIP space to enhance the semantic alignment between the segmented regions and the target object categories. More specifically, we propose Contrastive Prompt Learning and Class-associated Semantic Refinement to learn the prompts that adequately describe and suppress the image backgrounds associated with each target object category. In this way, our proposed framework is able to perform better semantic matching between object regions and the associated text labels, resulting in desired pseudo masks for training the segmentation model. The proposed SemPLeS framework achieves SOTA performance on the standard WSSS benchmarks, PASCAL VOC and MS COCO, and demonstrated interpretability with the semantic visualization of our learned prompts. The codes will be released.