Time-varying group formation control problems for general linear multi-agent systems with directed topologies are studied. Different from the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation, there could be multiple time-varying sub-formations. Firstly, a time-varying group formation protocol is constructed by local neighboring relative information. Then nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for the multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. Moreover, an approach to design the time-varying group formation protocol is proposed by solving an algebraic Riccati equation. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained theoretical results.