For low-altitude three-dimensional monitoring tasks involving heterogeneous unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), this paper proposes an adaptive neural-network-based cooperative control method enhanced with a prediction mechanism. A combined dynamic model is first established to describe both the underactuated 3-DOF UGV and the fully actuated 6-DOF UAV in a coordinated framework. A Kalman-filter-based state prediction module is then developed to forecast the UGV’s future positions using its real-time states, and the predicted trajectory is used as the tracking reference for the UAV. Furthermore, a Backstepping-based cooperative control law is constructed, where a radial basis function neural network (RBF-NN) is employed to approximate nonlinear uncertainties and external disturbances. Lyapunov analysis proves that the closed-loop system achieves semi-global uniform ultimate boundedness (SGUUB). Simulation results demonstrate the effectiveness of the proposed method in improving prediction accuracy and tracking stability.