For high-order continuous linear multi-agent systems, minimum-energy formation design methods with sampled-data communication were proposed. Based on local neighbouring information of multi-agent systems at sampling time, time-varying formation cooperative control protocol with global control energy consumption being considered was presented. By the state-space decomposition method, the time-varying formation problem of multi-agent systems was transformed into the stability problem of decomposed inconsensus subsystems. A formation feasible condition was constructed, and sufficient conditions for the design of time-varying formation under minimum-energy constraint can be obtained by the generalized eigenvalue approach, which ensures that the time-varying formation of multi-agent system can be realized under minimum-energy constraint. Theoretical results were verified by a numerical simulation, and the simulation results shows that the formation control method with minimum-energy constraints can effectively reduce the global control energy consumption of time-varying formation of multi-agent systems with sampled-data communication.