For a class of leader-following heterogeneous linear networked multi-agent systems, random network-induced delays and packet dropouts in the feedback and forward channels of each agent are considered, and an observer-based networked multi-agent cooperative output tracking control scheme is proposed. In this scheme, the leader agent produces a control prediction sequence and an output prediction sequence based on its delayed output and the system reference signal at each time instant. The former is used to actively compensate for random network-induced delays and packet dropouts in the control loop of the leader agent, and the latter is sent to following agents. Each following agent generates a control prediction sequence at each time instant based on its delayed output and the output prediction sequence received, which is employed to actively compensate for random network-induced delays and packet dropouts in the control loop of the following agent. Then the stability of the closed-loop networked multi-agent control system is analyzed. Finally, the effectiveness and feasibility of the proposed scheme are verified by practical experiments.