The integration of multi-source remote sensing data, bolstered by advancements in deep learning, has emerged as a pivotal strategy for enhancing land use and land cover (LULC) classification accuracy. However, current methods often fail to consider the numerous prior knowledge of remote sensing images and the characteristics of heterogeneous remote sensing data, resulting in data loss between different modalities and the loss of a significant amount of useful information, thus affecting classification accuracy. To tackle these challenges, this paper proposes a LULC classification method based on remote sensing data that combines a Transformer and cross-pseudo-siamese learning deep neural network (TCPSNet). It first conducts shallow feature extraction in a dynamic multi-scale manner, fully leveraging the prior information of remote sensing data. Then, it further models deep features through the multimodal cross-attention module (MCAM) and cross-pseudo-siamese learning module (CPSLM). Finally, it achieves comprehensive fusion of local and global features through feature-level fusion and decision-level fusion combinations. Extensive experiments on datasets such as Trento, Houston 2013, Augsburg, MUUFL and Berlin demonstrate the superior performance of the proposed TCPSNet. The overall accuracy (OA) of the network on the Trento, Houston 2013 and Augsburg datasets is of 99.76%, 99.92%, 97.41%, 87.97% and 97.96%, respectively.