The increasing use of static converters in the industrial sector is the main cause of the power grid energy quality degradation. These kinds of converters are characterized by their absorption of non-sinusoidal currents and their functioning under a degraded power factor. The purpose of this paper is to improve the power grid quality supplying a polluting load via the three-phase shunt active power filter (SAPF). To do this, an advanced approach based on a combination of the adaptive technique and the fuzzy logic theory was applied to ensure an advanced control of the SAPF. The three current hysteresis comparators and the voltage regulator of the conventional filter control have been replaced respectively by three fuzzy adaptive hysteresis regulators and a fuzzy controller. The smart control law made up of these advanced regulators makes it possible to guarantee an operation of the filter with improved performances. The effectiveness of the developed control strategy for the studied SAPF was tested and evaluated under the MATLAB/Simulink software. The obtained results show that the DC bus voltage is maintained perfectly at its imposed reference; the source currents are presented by a sinusoidal form; the power factor is very close to the unity and the two-level DC/AC converter of the SAPF operates under a fixed switching frequency.