Making eye contact is a most important prerequisite function of humans to initiate a conversation with others. However, it is not an easy task for a robot to make eye contact with a human if they are not facing each other initially or the human is intensely engaged his/her task. If the robot would like to start communication with a particular person, it should turn its gaze to that person and make eye contact with him/her. However, such a turning action alone is not enough to set up an eye contact phenomenon in all cases. Therefore, the robot should perform some stronger actions in some situations so that it can attract the target person before meeting his/her gaze. In this paper, we proposed a conceptual model of eye contact for social robots consisting of two phases: capturing attention and ensuring the attention capture. Evaluation experiments with human participants reveal the effectiveness of the proposed model in four viewing situations, namely, central field of view, near peripheral field of view, far peripheral field of view, and out of field of view.