This paper proposes an adaptive range estimation method in a perspective vision system using neural networks (NN). With a universal function approximation property of the NN, this study first defines the NN-based range value and the adaptive observer to determine the distance is designed with the known object motion, i.e., translational and rotational velocities. To remove the uncertainty between the true range and the estimated value, the proposed estimator utilizes a saturation function with a time-varying gain. The adaptive rules of the weight parameters of the NN and time-varying gain are derived using Lyapunov stability theory and the overall closed-loop stability is proven by introducing a deadzoned estimation error, which is composed of the estimation error and the saturation function. Finally, to validate the performance of the proposed method, experiments are conducted for the estimation of the relative distance between a target and a camera mounted on a multirotor unmanned aerial vehicle with an inertial measurement unit and a motion capture system.