This paper presents a robust controller design for three-phase grid-connected solar PhotoVoltaic (PV) systems to control active power. The controller is designed based on a nonlinear adaptive backstepping approach and the robustness of the proposed scheme is ensured by considering parametric uncertainties as well as external disturbances. In the proposed control strategy, all parameters within the grid-connected solar PV systems are considered as unknown which are then estimated through the adaptation laws. These estimated parameters along with external disturbances are incorporated into the controller to ensure the overall stability of the whole system through the formulation of Control Lyapunov Functions (CLFs). An Incremental Conductance (IC) method is used to track the Maximum Power Point (MPP) at which a constant DC-link voltage is maintained and this voltage is used to obtain the reference value of the current which is used for active power control. A three-phase grid-connected solar PV is used to evaluate the performance of the proposed control scheme under different operating conditions. The simulations results clearly indicate the robustness of the proposed scheme in terms of injecting active power into the grid and improving power quality as compared to an existing adaptive backstepping controller.