Learning modality-fused representations and processing unaligned multimodal sequences are meaningful and challenging in multimodal emotion recognition. Existing approaches use directional pairwise attention or a message hub to fuse language, visual, and audio modalities. However, those approaches introduce information redundancy when fusing features and are inefficient without considering the complementarity of modalities. In this paper, we propose an efficient neural network to learn modality-fused representations with CB-Transformer (LMR-CBT) for multimodal emotion recognition from unaligned multimodal sequences. Specifically, we first perform feature extraction for the three modalities respectively to obtain the local structure of the sequences. Then, we design a novel transformer with cross-modal blocks (CB-Transformer) that enables complementary learning of different modalities, mainly divided into local temporal learning,cross-modal feature fusion and global self-attention representations. In addition, we splice the fused features with the original features to classify the emotions of the sequences. Finally, we conduct word-aligned and unaligned experiments on three challenging datasets, IEMOCAP, CMU-MOSI, and CMU-MOSEI. The experimental results show the superiority and efficiency of our proposed method in both settings. Compared with the mainstream methods, our approach reaches the state-of-the-art with a minimum number of parameters.