To address the stable formation tracking problem of quadrotor UAVs (unmanned aerial vehicles) under external wind disturbances and internal unmodeled dynamics, a predefined-time nonsingular adaptive anti-disturbance formation control method based on RBF (radial basis function) neural networks was proposed. First, a predefined-time reference signal estimator was constructed to generate and adjust the desired trajectory. Then, a predefined-time filter was introduced into the virtual control law, and a continuously differentiable switching function was designed to avoid the singularity issue caused by power-integrator terms in conventional backstepping. Furthermore, RBF neural networks were employed to approximate the unmodeled dynamics, while a predefined-time disturbance observer was developed to jointly estimate and compensate for wind disturbances and neural network approximation errors. Finally, through a hierarchical design consisting of the reference estimator, position-loop controller, and attitude-loop controller, predefined-time stable formation tracking of quadrotor UAVs was achieved. Experimental results demonstrate that the method can still ensure fast convergence of the system under various wind disturbances and uncertainties, validating the effectiveness and superiority of the proposed control strategy.