We developed an autonomous human-like guide robot for a science museum. Its identifies individuals, estimates the exhibits at which visitors are looking, and proactively approaches them to provide explanations with gaze autonomously, using our new approach called speak-and-retreat interaction. The robot also performs such relation-building behaviors as greeting visitors by their names and expressing a friendlier attitude to repeat visitors. We conducted a field study in a science museum at which our system basically operated autonomously and the visitors responded quite positively. First-time visitors on average interacted with the robot for about 9 min, and 94.74% expressed a desire to interact with it again in the future. Repeat visitors noticed its relation-building capability and perceived a closer relationship with it.