This paper proposes a power-voltage control scheme of a grid-connected converter based on nonlinear optimization. Power tracking is formulated into a min-max optimization problem and its subproblem is stated in sequential quadratic programming (SQP). The optimal operating point to track power reference is derived in real time by solving SQP, while satisfying current limitation and voltage control constraint at the point of common coupling (PCC). Receiving the reference for the power and voltage control from a higher level control system, the proposed power-voltage controller is integrated into the conventional grid-following (GFL) control structure. Thereby, accurate, stable, and fast power control characteristic of GFL control is implemented in weak grid without complicated tuning or modification of phase-locked loop (PLL) and the conventional control scheme. The performance of the proposed method is demonstrated through experimental results.