Harmonic elimination in three-phase power systems due to non-linear loads in electrical grids is an essential topic in power quality nowadays. The rise of electronics and electrical devices increases the sensitivity of the network. The current research approaches this topic by proposing the design and simulation of a neural network with a modified LMS (Least Mean Square) algorithm, including variable step-size in the cost function to achieve faster convergence and overcoming problems in drifting parameters. We use a three-phase active power filter (APF) that relies on a current compensation control for testing purposes. The APF consists of a hysteresis control block and a current-controlled voltage source inverter computed by our enhanced ADALINE (Adaptative Linear Element) neural network. Finally, a comparison is made with another algorithm based on non-variable step size. Results show a 3 % reduction in THD (Total Harmonic Distortion) parameter and a 0.2 s faster response time, concluding the improvement in performance parameters of the power system.