This paper addresses a predictive cloud control problem for a linear multiagent system with random network delays and noises. To reduce communication cost, a stochastic event-triggered schedule is introduced to decide whether current measurements need to be transmitted. An optimal state estimation algorithm is designed to compensate random network delays in the feedback channel. Subsequently, a predictive cloud control scheme is proposed for the multiagent system to achieve both stability and consensus. Simultaneously, random network delays in the forward channel is compensated actively. Sufficient and necessary conditions of stability and consensus for the closed-loop multiagent system are derived. Finally, a numerical example is provided to verify correctness and effectiveness of the proposed methods.