Sequential recommendation can establish user behavior sequences based on the historical interaction records between users and items to dynamically model user preferences. In sequential recommendation, accurate modeling of both the long and short-term interests of users is the key to accurate recommendations. To address the issue of existing models’ inability to effectively capture both long and short-term interests, this paper proposed a Temporal Convolutional Network and Gated Recurrent Unit-based Sequential Recommendation Model with Attention Mechanism (TGAM-SR) to address existing models’ inability to effectively capture both long and short-term interests. Firstly, TGAM-SR uses a TCN and attention mechanism to model long-term interests, fully exploring user long-term interest information. At the same time, it uses a low-complexity GRU and multi-head self-attention mechanism to model short-term interests. Lastly, the attention mechanism calculates the weights of both long and short-term interests, and a gated fusion module is employed to integrate these interests. Experimental results show that compared to popular and newer sequential recommendation models, TGAM-SR exhibits superior performance in metrics such as hit rate and recall rate.