Large-scale pre-trained Vision-Language Models (VLMs), such as CLIP, establish the correlation between texts and images, achieving remarkable success on various downstream tasks with fine-tuning. In existing fine-tuning methods, the class-specific text description is matched against the whole image. We recognize that this whole image matching is not effective since images from the same class often contain a set of different semantic objects, and an object further consists of a set of semantic parts or concepts. Individual semantic parts or concepts may appear in image samples from different classes. To address this issue, in this paper, we develop a new method called cross-model concept learning and inference (CCLI). Using the powerful text-image correlation capability of CLIP, our method automatically learns a large set of distinctive visual concepts from images using a set of semantic text concepts. Based on these visual concepts, we construct a discriminative representation of images and learn a concept inference network to perform downstream image classification tasks, such as few-shot learning and domain generalization. Extensive experimental results demonstrate that our CCLI method is able to improve the performance upon the current state-of-the-art methods by large margins, for example, by up to 8.0% improvement on few-shot learning and by up to 1.3% for domain generalization.