Semantic-rich speech emotion recognition has a high degree of popularity in a range of areas. Speech emotion recognition aims to recognize human emotional states from utterances containing both acoustic and linguistic information. Since both textual and audio patterns play essential roles in speech emotion recognition (SER) tasks, various works have proposed novel modality fusing methods to exploit text and audio signals effectively. However, most of the high performance of existing models is dependent on a great number of learnable parameters, and they can only work well on data with fixed length. Therefore, minimizing computational overhead and improving generalization to unseen data with various lengths while maintaining a certain level of recognition accuracy is an urgent application problem. In this paper, we propose LGCCT, a light gated and crossed complementation transformer for multimodal speech emotion recognition. First, our model is capable of fusing modality information efficiently. Specifically, the acoustic features are extracted by CNN-BiLSTM while the textual features are extracted by BiLSTM. The modality-fused representation is then generated by the cross-attention module. We apply the gate-control mechanism to achieve the balanced integration of the original modality representation and the modality-fused representation. Second, the degree of attention focus can be considered, as the uncertainty and the entropy of the same token should converge to the same value independent of the length. To improve the generalization of the model to various testing-sequence lengths, we adopt the length-scaled dot product to calculate the attention score, which can be interpreted from a theoretical view of entropy. The operation of the length-scaled dot product is cheap but effective. Experiments are conducted on the benchmark dataset CMU-MOSEI. Compared to the baseline models, our model achieves an 81.0% F1 score with only 0.432 M parameters, showing an improvement in the balance between performance and the number of parameters. Moreover, the ablation study signifies the effectiveness of our model and its scalability to various input-sequence lengths, wherein the relative improvement is almost 20% of the baseline without a length-scaled dot product.