N4-acetylcytidine (ac4C) is a post-transcriptional modification in mRNA that is critical in mRNA translation in terms of stability and regulation. In the past few years, numerous approaches employing convolutional neural networks (CNN) and Transformer have been proposed for the identification of ac4C sites, with each variety of approaches processing distinct characteristics. CNN-based methods excels at extracting local features and positional information, whereas Transformer-based ones stands out in establishing long-range dependencies and generating global representations. Given the importance of both local and global features in mRNA ac4C sites identification, we propose a novel method termed TransC-ac4C which combines CNN and Transformer together for enhancing the feature extraction capability and improving the identification accuracy. Five different feature encoding strategies (One-hot, NCP, ND, EIIP, and K-mer) are employed to generate the mRNA sequence representations, in which way the sequence attributes and physical and chemical properties of the sequences can be embedded. To strengthen the relevance of features, we construct a novel feature fusion method. Firstly, the CNN is employed to process five single features, stitch them together and feed them to the Transformer layer. Then, our approach employs CNN to extract local features and Transformer subsequently to establish global long-range dependencies among extracted features. We use 5-fold cross-validation to evaluate the model, and the evaluation indicators are significantly improved. The prediction accuracy of the two datasets is as high as 81.42.