<abstract> <p>Improving the efficiency of human-computer interaction is one of the critical goals of intelligent aircraft cockpit research. The gaze interaction control method can vastly reduce the manual operation of operators and improve the intellectual level of human-computer interaction. Eye-tracking is the basis of sight interaction, so the performance of eye-tracking will directly affect the outcome of gaze interaction. This paper presents an eye-tracking method suitable for human-computer interaction in an aircraft cockpit, which can now estimate the gaze position of operators on multiple screens based on face images. We use a multi-camera system to capture facial images, so that operators are not limited by the angle of head rotation. To improve the accuracy of gaze estimation, we have constructed a hybrid network. One branch uses the transformer framework to extract the global features of the face images; the other branch uses a convolutional neural network structure to extract the local features of the face images. Finally, the extracted features of the two branches are fused for eye-tracking. The experimental results show that the proposed method not only solves the problem of limited head movement for operators but also improves the accuracy of gaze estimation. In addition, our method has a capture rate of more than 80% for targets of different sizes, which is better than the other compared models.</p> </abstract>