In this article, the specified-time affine formation maneuver control (AFMC) problem is studied with a leader–follower structure over a directed communication network. First, by means of Pontraygin's maximum principle and motion-planning techniques, a specified-time AFMC algorithm is designed for the second-integrator systems with dynamic leaders, which can lead the followers to achieve the desired affine formation at a specified settling time according to mission requirements and environmental constraints. Furthermore, the specified-time AFMC problem without velocity measurement is studied. The global convergence and stability of the closed-loop system with proposed control algorithms are analyzed. Compared with the existing finite-time AFMC algorithms, a prominent advantage of the proposed specified-time algorithms is that the convergence moment of AFMC can be accurately scheduled and appointed in advance. Finally, an example is simulated to verify the effectiveness of the proposed algorithms.