This paper presents a nonlinear control scheme to regulate the dc-link voltage for extracting the maximum power from PV system and the current to control the amount of injected power into the grid. The controller is designed using an adaptive backstepping technique by considering the parameters of the system as totally unknown. The control of power injection into the grid requires the regulation of active and reactive components of the output current of the inverter in order to control active and reactive power, respectively. The proposed controller is adaptive to unknown parameters of grid-connected solar photovoltaic (PV) systems and these parameters are estimated through the adaptation laws while guaranteeing the extraction of maximum power from the PV system and delivering appropriate active and reactive power into the grid. The overall stability of the whole system is analyzed based on the formulation of control Lyapunov functions (CLFs). Finally, the performance of the designed controller is tested on a three-phase grid-connected PV system under changeing environmental conditions and the result is also compared with an existing backstepping controller in terms of improving power quality. Simulation results indicate the robustness of the proposed scheme under changing atmospheric conditions.