<p>Given the transient characteristics of terminal guidance, achieving rapid error convergence is essential, particularly in cases involving high initial deviations. In this paper, a unified predefined-time cooperative guidance law for leader-following missiles is proposed that the missiles can simultaneously attack a target with impact time and impact angle constraints. Firstly, a unified Lyapunov-like characterization for predefined-time is introduced to designed the cooperative guidance law. To enable accurate target engagement at a specified impact time, the leader’s guidance law along the line-of-sight (LOS) direction is formulated. Moreover, the followers’ LOS guidance laws are designed using the time consensus error function and unified predefined-time theory. By leveraging inter-missile communication, both the leader’s and followers’ time-to-go rapidly converge within a predefined time. Subsequently, guidance laws governing the LOS elevation and azimuth directions are formulated to satisfy expected impact angle requirements. The LOS angles of all missiles exhibit predefined-time convergence to their target values, enabling omnidirectional target engagement. Meanwhile, the predefined-time stability is rigorously proved through the Lyapunov theory. Finally, the effectiveness of the cooperative guidance law is demonstrated by several sets of numerical simulation experiments.</p>