For pediatric rehabilitation, obtaining accurate coupled human-exoskeleton system models is challenging due to unknown model parameters caused by children’s dynamic growth and development. These factors make it difficult to establish precise and standardized models for exoskeleton control. Additionally, external disturbances, such as unpredictable movements or involuntary muscle contractions, further complicate the control process that must be addressed. This work presents the computed torque control (CTC) scheme compensated by a radial basis function neural network (RBFNN) for an uncertain lower-limb exoskeleton system. Primarily, the design, hardware architecture, and experimental procedure of a pediatric exoskeleton are briefly demonstrated. Thereafter, the proposed adaptive RBFNN-CTC (ARBFNN-CTC) is highlighted, where the adaptation of network weights depends on the Gaussian function and the Lyapunov equation. The adaptive RBFNN estimates the unknown model dynamics and compensates the CTC for the effective gait tracking of the coupled system in passive-assist mode. A Lyapunov stability is presented to ensure the convergence of error states into a significantly small domain. Finally, an experimental study with a pediatric subject (12 years) is carried out to investigate the effectiveness of the proposed control scheme. The gait tracking results show that the ARBFNN-CTC outperforms the traditional CTC by nearly 40% over three gait cycles. Furthermore, the proposed approach’s generalizability is validated across various gait cycles, especially at 3, 10, 20, and 30 cycles. The high correlation coefficients of 0.996, 0.997, and 0.999 for the hip, knee, and ankle joints, respectively, at thirty gait cycles, highlight the potential of the ARBFNN-CTC scheme in achieving effective and consistent gait training outcomes over extended periods.