Classification of pathological images is the basis for automatic cancer diagnosis. Despite that deep learning methods have achieved remarkable performance, they heavily rely on labeled data, demanding extensive human annotation efforts. In this study, we present a novel human annotation-free method by leveraging pre-trained Vision-Language Models (VLMs). Without human annotation, pseudo-labels of the training set are obtained by utilizing the zero-shot inference capabilities of VLM, which may contain a lot of noise due to the domain gap between the pre-training and target datasets. To address this issue, we introduce VLM-CPL, a novel approach that contains two noisy label filtering techniques with a semi-supervised learning strategy. Specifically, we first obtain prompt-based pseudo-labels with uncertainty estimation by zero-shot inference with the VLM using multiple augmented views of an input. Then, by leveraging the feature representation ability of VLM, we obtain feature-based pseudo-labels via sample clustering in the feature space. Prompt-feature consensus is introduced to select reliable samples based on the consensus between the two types of pseudo-labels. We further propose High-confidence Cross Supervision by to learn from samples with reliable pseudo-labels and the remaining unlabeled samples. Additionally, we present an innovative open-set prompting strategy that filters irrelevant patches from whole slides to enhance the quality of selected patches. Experimental results on five public pathological image datasets for patch-level and slide-level classification showed that our method substantially outperformed zero-shot classification by VLMs, and was superior to existing noisy label learning methods. The code is publicly available at https://github.com/HiLab-git/VLM-CPL