Gaze estimation plays a crucial role in interactive applications. Recent advancements in deep learning have significantly enhanced appearance-based methods. However, existing approaches often focus on one eye and do not consider binocular gaze, overlooking a fundamental principle of human gaze: the convergence of gaze based on binocular cooperative information. To address this gap, we introduce BCNet, a network for binocular gaze estimation. Specifically, we develop the binocular-chiasm module to facilitate feature exchange between the two eyes and design a binocular-geometry loss that leverages gaze spatial geometry to improve convergence during fixation. Additionally, our person-specific analysis further reduces gaze estimation errors for individual users. Our method registers a \(4.8\%\) improvement on the MPIIGaze dataset over existing methods and achieves competitive results on the EyeDiap dataset. Experiments with noised data underscore the robustness of our proposed approach.