For single-integrator kinematics of multi-agent systems with connected bipartite topology, the system’s weighted group-consensus problem with/without time-delay is investigated. A decentralized and coordinated control protocol is designed. Based on the matrix theory and the graph theory, it is proved that the multi-agent systems can converge to the arbitrary prescribed weighted state. For the cases with time-delay, a upper bound on the maximum time-delay that the system can tolerate is obtained by using the gerschgorin theorem and Nyquist’s criterion. The simulation examples show the correctness of the obtained results.