In order to handle the situation where a mobile robot overlaps an area that a person is paying attention to in human-robot integration scenario, a socially-aware navigation method that considers human gaze-related area constraints is proposed. Firstly, the gaze state is determined and a horizon-interaction model is constructed based on the perceived gaze direction and gaze target. Then, the extended social forces including sight line electrostatic force, sight line magnetic deflection force, and potential field force related to the horizon-interaction model, are introduced in reference to electromagnetic fields and limit cycle theory, to model the relationship between human gaze and robot behavior. This design leads the robot to avoid or approach regions of interest to humans under social norms according to the task type, which enhances the social attributes of the service robot while ensuring the psychological comfort of human. The qualitative and quantitative analysis of the simulation section and the questionnaire evaluation demonstrate the necessity of introducing human gaze-related area constraints in socially-aware navigation of a robot, and validates the efficacy and viability of the proposed navigation method.