Nonverbal and noncontact behaviors play a significant role in allowing service robots to structure their interactions with humans. In this paper, a novel human-mimic mechanism of robot navigational skills was proposed for developing socially acceptable robotic etiquette. Based on the sociological and physiological concerns of interpersonal interactions in movement, several criteria in navigation were represented by constraints and incorporated into a unified probabilistic cost grid for safe motion planning and control, followed by an emphasis on the prediction of the human's movement for adjusting the robot's pre-collision navigational strategy. The human motion prediction utilizes a clustering-based algorithm for modeling human indoor motion patterns as well as the combination of the long-term and short-term tendency prediction that takes into account the uncertainties of both velocity and heading direction. Both simulation and real-world experiments verified the effectiveness and reliability of the method to ensure human safety and comfort in navigation. A statistical user trial study was also given to validate the users' favorable views of the human-friendly navigational behavior.