This brief focuses on solving the tracking problem of swarm robots with a non-cooperative target, where two core issues namely non-cooperative target and cross-domain collaboration are both taken into account. In order to solve the former issue, the trajectory of the non-cooperative target is constructed by a network model. This is more superior than the target system matrix observer-based method that adopted extensively in literature, as the latter one will cause the self-loop problem. Besides, the target information is no longer required in solving the regulation equation. Furthermore, a fixed-time cross-domain control method merely relying on outputs of a robot and its neighbours is proposed. Namely, the network-based fixed-time control method proposed in this brief is fully distributed without self-loop and requirement of the non-cooperative target’s system matrix. With the proposed controller, the cross-domain robots are able to successfully track a non-cooperative target within a fixed time, which is also verified by some numerical simulations.