Semi-supervised semantic segmentation (SSS) has recently gained increasing research interest as it can reduce the requirement for large-scale fully-annotated training data. The current methods often suffer from the confirmation bias from the pseudo-labelling process, which can be alleviated by the co-training framework. The current co-training-based SSS methods rely on hand-crafted perturbations to prevent the different sub-nets from collapsing into each other, but these artificial perturbations cannot lead to the optimal solution. In this work, we propose a new conflict-based cross-view consistency (CCVC) method based on a two-branch co-training framework which aims at enforcing the two sub-nets to learn informative features from irrelevant views. In particular, we first propose a new cross-view consistency (CVC) strategy that encourages the two sub-nets to learn distinct features from the same input by introducing a feature discrepancy loss, while these distinct features are expected to generate consistent prediction scores of the input. The CVC strategy helps to prevent the two sub-nets from stepping into the collapse. In addition, we further propose a conflict-based pseudo-labelling (CPL) method to guarantee the model will learn more useful information from conflicting predictions, which will lead to a stable training process. We validate our new CCVC approach on the SSS benchmark datasets where our method achieves new state-of-the-art performance. Our code is available at https://github.com/xiaoyao3302/CCVC.