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This paper mainly studies a cooperative circumnavigation control problem of multiple non-holonomic robots for multiple dynamic targets. First, an extended circular multiple target configuration is ensured to drive robots to generate the target defense mission. Then, a distributed time-varying circular formation control protocol is proposed based on the relative position and orientation of nodes, while its neighbors are used to escort target under the predetermined geometric distribution cooperatively. Note that the center and enclosing radius of the dynamic targets are time-varying. Specially, by designing virtual signal variables into the desired velocity and angular velocity loops, a new distributed control strategy with the time-varying escorting radius is proposed via backstepping technology. Under mild assumptions about the target velocity, the proposed formation controller can enforce the multi-robot to asymptotically converge on a guided circle centered on the multi-target, while maintaining a predetermined geometric formation configuration. Lyapunov analysis verity that all errors can be stabilized to origin asymptotically, and simulations proof the feasibility of the proposed control scheme.