This paper studies the leader–follower circumnavigation problem of two non-holonomic robots using just an angular velocity adjustment. Specifically, two robots orbit around a stationary target along a circle trajectory with a pre-specified spacing distance apart and velocity. However, two robots have no global positioning information and cannot localize the target. Instead, they can just obtain real-time distance-related information with respect to surrounding objects. Based on a leader–follower protocol framework, a distance-based control algorithm is developed to generate saturated control inputs for two robots. Besides, the criteria of the control parameters and initial states are explicitly established. It is demonstrated in detail that, under the established criteria, the developed distance-based control algorithm enables two robots to fulfill the leader–follower circumnavigation objective. Simulation and experiment are carried out to assess and demonstrate the effectiveness of the proposed theoretical results.