This paper focuses on the guidance problem of cooperatively attacking an aggressively maneuvering target via multiple UAVs. A cooperative guidance law is devised with a long short-term memory (LSTM) neural network employed to predict the target's maneuver to achieve accuracy impact. Firstly, the motion normal to the line-of-sight and motion along the line-of-sight is modeled separately with disturbances caused by target maneuvers considered. Secondly, a LSTM neural network is designed to predict disturbances caused by target maneuvers. Then, the guidance laws normal or along the LOS are designed separately based on the theory of sliding-mode control, in which the guidance law along the line-of-sight direction is used to achieve the same impact time of the UAVs and the guidance law normal to the line-of-sight is employed to drive the angle of view to the desired value. Finally, simulations are conducted in the scenario of multi-UAV cooperatively attacking an aggressively maneuvering target. The simulation results show that the designed LSTM neural network can effectively predict disturbances caused by target maneuvers, and the proposed cooperative guidance laws can satisfy the constraint of line-of-sight angle and achieve a better cooperation.