This paper investigates the safe-circumnavigation control issue for multiple-targets’ geometric center in 3D space, where agent relies solely on bearing information. Firstly, a new estimator applicable in 3D space is proposed, and it is proved that this estimator can converge the estimated positions to fixed points. Secondly, a novel controller is designed, and the analysis show that under the controller, the agent can circumnavigate the geometric center of these fixed points in the expected manner. Moreover, by using the contradiction, it is demonstrated that these fixed points are the actual positions of the targets. That is to say, it is proved that under the joint action of the estimator and the controller, the agent can achieve circumnavigating the targets. And some sufficient conditions for avoiding the collision between the agent and the targets are derived. Finally, a numerical simulation is employed to verify the conclusions of this paper.