In view of the complex and dynamic industrial application scenarios in intelligent manufacturing and the growing demand for enhanced intelligence in industrial robots, this paper proposes a Transformer-based imitation learning control strategy. First, a demonstration robot model is designed and an imitation learning experimental platform is established to simplify the acquisition of expert demonstration data and improve efficiency. Second, a gripper-based action chunking with Transformers (GACT) model is proposed, which incorporates a binary cross-entropy loss function tailored to pneumatic gripper states and introduces an independent cross-attention mechanism dedicated to gripper states. Third, simulations are conducted in the MuJoCo environment, and ablation studies are performed to evaluate the effectiveness of the proposed components. Finally, real-world experiments are carried out on a KUKA industrial robot. Simulation results show that the GACT model achieves higher task success rates and trajectory accuracy than the baseline and its variants. Experimental results further confirm that the GACT can effectively realize precise motion control of industrial robots.