This paper introduces an efficient control approach to enhance harmonics mitigation performance of the Shunt Active Power Filter(SAPF). This approach is based on adaptive filters favored by their built-in automatic parameters adaptation capability. The proposed filter, which uses a Variable Leaky Least Mean Square (VLLMS) adaptation, is applied with a modified instantaneous power PQ theory. This enhances its dynamic performance over the use of conventional time-invariant filters, and overcomes its limitations in the presence of non-sinusoidal voltage conditions. The studied SAPF model is simulated in MATLAB/SIMULINK with combinations of non-linear and unbalanced loads. Simulation results indicate a significant improvement in the transient response to less than a quarter of a cycle in its worst case, on top of additional improvements in the steady-state THD value. Moreover, the algorithm's computation efficiency evaluated in an embedded hardware prototype has given a fast execution time of 1.4µs .