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Guaranteed-performance time-varying formation analysis and design problems for general high-order swarm systems with communication constraints are investigated. First, a guaranteed-performance time-varying formation control protocol is proposed by using the intermittent relative local information, and the performance function is introduced to guarantee the formation regulation performance among neighboring agents. An explicit presentation of the formation center function is presented to describe the movement trajectory of the formation as a whole. Then, sufficient conditions for guaranteed-performance time-varying formation analysis and design are respectively given by linear matrix inequality techniques, and a guaranteed-performance cost is determined meanwhile. When the desired guaranteed-performance time-varying formation satisfies the time-varying formation feasibility condition, swarm systems with communication constraints can achieve the guaranteed-performance time-varying formation by designing the gain matrix of the guaranteed-performance time-varying formation control protocol if the nominal coverage rate is larger than a positive threshold. Finally, a numerical simulation is shown to illustrate theoretical results.