The practical fixed-time affine formation (PFAF) control problem for multi-agent systems is studied in this brief. The tasks of formation assembly, transformation and time-varying maneuver are able to be completed by affine formation control technique based on stress matrix flexibly and conveniently. Based on time-based generators (TBG) techniques, two fixed-time control laws are designed for leaderless and leader-follower affine formation control problems, respectively. Compared with the existing finite-time affine formation control laws, the convergence times of the proposed control laws in this brief are independent of the system’s initial states. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed control laws.