In this study, adaptive time-varying group formation control for second-order multi-agent systems with an undirected topology is studied. First, a conventional multi-group adaptive time-varying formation control protocol is presented, and the stability of the system is analyzed based on the Lyapunov method. Considering that traditional methods of dealing with nonlinear dynamics cannot be directly applied to the time-varying formation problem, the parameter estimation method is used to track the unknown internal nonlinear dynamics of an agent. A virtual leader and filter are introduced to solve the problem of variable derivation and repeated derivation of the system state, and the adaptive rate of time-varying formation converges to a stable value. Finally, the feasibility of the results is verified using two simulation results.