Learning-based control strategies can significantly streamline the process of modeling robotic arms and adjusting control parameters, making them widely used in robotic arm motion control. However, the existing learning-based motion control strategies suffer from insufficient feature extraction, resulting in limited prediction accuracy. To address this problem, this paper proposes a robotic arm motion control strategy based on a cascaded feature-enhanced elastic-net broad learning system (CFE-EN-BLS), which improves the trajectory tracking accuracy of robotic arms. Firstly, a motion control strategy of the cascaded feature-enhanced broad learning system (CFE-BLS) is constructed to fully extract data features to improve joint position-tracking accuracy. Secondly, combined with elastic-net regression, a motion control strategy for the robotic arm based on CFE-EN-BLS is designed to reduce feature redundancy. Finally, the learning parameters of the proposed control strategy are constrained by incorporating Lyapunov theory to bolster the convergence of the control strategy. Simulation and experimental results show that the proposed control strategy can effectively extract data features and achieve high-precision trajectory tracking control of the robotic arm. The position tracking mean-squared-error (MSE) and root-mean-squared-error (RMSE) are 0.00174 and 0.04167, respectively, which represent reductions of 74.71% and 49.76% compared to the existing method.