This paper studied the distributed adaptive time-varying formation problem for general linear multi-agent systems over a directed topology. First of all, some conditions to achieve distributed time-varying formations are given, which describe a feasible time-varying formation set. Second, a distributed adaptive algorithm is proposed for achieving fully distributed time-varying formation, which is independent of any global information. By analyzing the Lyapunov stability, we prove that the proposed distributed adaptive algorithm can guarantee the multiple agents achieving the required time-varying formation. Finally, a numerical example is given to verify the theoretical results.