Massive integration of converter-based renewable energy sources into power systems through weak AC grid has become a dilemma in recent years. This paper investigates the design of a robust nonlinear multi-input-multi-output (MIMO) controller for voltage source converters (VSCs) connected to weak AC grids. Feedback linearization method is used to find the controller equations and design the inputs to regulate the active power and output voltage of the converter. With this approach, the controller is designed in a way that the grid impedance impact on the stability of the converter system is significantly reduced. The robustness of the proposed controller is evaluated using time-domain simulations of a grid-connected VSC enhanced with the nonlinear controller in various case studies. The results illustrate a significant improvement compared to existing approaches.