For high-order continuous linear multi-agent systems, a minimum-energy formation design method with sampled-data communication was proposed. Based on local neighboring information of multi-agent systems at sampling time, a 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 non-consensus subsystems. A formation feasible condition was constructed, and sufficient conditions for the design of time-varying formation under minimum-energy constraints were obtained by the generalized eigenvalue approach, which ensured that the time-varying formation of multi-agent systems could be realized under minimum-energy constraints. Theoretical results were verified by a numerical simulation, and simulation results show 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.