T cell receptors (TCRs) selectively bind to antigens to fight pathogens with specific immunity. Current tools focus on the nature of amino acids within sequences and take less into account the nature of amino acids far apart and the relationship between sequences, leading to significant differences in the results from different datasets. We propose TPBTE, a model based on convolutional Transformer for Predicting the Binding of TCR to Epitope. It takes epitope sequences and the complementary decision region 3 (CDR3) sequences of TCRβ chain as inputs. And it uses a convolutional attention mechanism to learn amino acid representations between different positions of the sequences based on learning local features of the sequences. At the same time, it uses cross attention to learn the interaction information between TCR sequences and epitope sequences. A comprehensive evaluation of the TCR-epitope data shows that the average area under the curve of TPBTE outperforms the baseline model, and demonstrate an intentional performance. In addition, TPBTE can give the probability of binding TCR to epitopes, which can be used as the first step of epitope screening, narrowing the scope of epitope search and reducing the time of epitope search.