This work develops a predictive pursuer guidance algorithm that generates sub-optimal guidance commands based on evader acceleration predictions produced by a recurrent neural network. Due to their reactive nature, common guidance laws such as proportional navigation (PN) or augmented proportional navigation (APN) have either restricted capture region or poor engagement performance against highly maneuverable evader. On the other hand, even though predictive guidance laws tend to have better performance against highly maneuverable evaders, they assume full or partial knowledge of the evader dynamics, which can be a limiting assumption. To address aforementioned shortcomings of the previous efforts, this paper proposes a pursuer guidance algorithm in which the evader’s future acceleration commands are predicted in a finite time horizon by employing a network of gated recurrent units (GRU), which are trained on a library of exemplary evader dynamics. Predicted evader commands are then assigned within the constraints of a transcribed finite-horizon optimal control problem, cast as a nonlinear program (NLP). Once the NLP is solved over a finite time horizon, the pursuer acceleration solution for the next time step is considered as the pursuer guidance command. Simulation studies are conducted for interception of an agile evasive evader to compare the current work against the conventional laws mentioned above and a modern counterpart. Results demonstrate that the proposed guidance law is superior to compared approaches in terms of guidance performance metrics such as miss distance.