This paper proposes a new robust adaptive controller for LCL filter based shunt active power filters in order to solve the control problems of high overshoot and large settling time in the DC link voltage. To this end, the second order sliding mode with the adaptive gain super-twisting control law and proportional-resonant controllers with active damping are used in the DC bus voltage control loop and d-q axis current control loops respectively. The control objectives are fourfold: (I) driving the DC bus voltage to a reference signal; (ii) forcing the d-q axis current errors to zero; (iii) assuring a satisfactory power factor correction and a high harmonic performance in relation to the AC source; and (iv) eliminating the chattering effect. In the closed loop control system, three phase grid currents, LCL capacitor currents and the DC link voltage are available for feedback. As a result, the proposed controller has the advantages of zero overshoot response and fast acting chattering-free behavior. Results of experimental studies prove that the proposed control system guarantees to track reference signals with a high harmonic performance despite external disturbance uncertainties. (C) 2015 Elsevier Ltd. All rights reserved.