This article proposes adaptive continuouscontrol-set model predictive control (CCS-MPC) for threephase LCL-filter grid-tied inverters in the stationary frame. The proposed control provides stability against the LCLfilter resonance and removes the need for active damping or passive damping. Furthermore, it can track sinusoidal references in the stationary frame close to zero offsets. Inductance variation of a grid is a challenging issue, which can shift the LCL-filter resonance. Even though CCS-MPC generally has good stability for parameter mismatches, the control is optimized for the nominal value of the parameters. A relatively large variation may deteriorate the performance of the control and cause instability in the closed-loop system. To solve this problem, the concept of CCS-MPC is developed to work with a variety of the gridinductance changes. The controller coefficients are chosen with a sensitivity analysis to provide enough gain margins and phase margins for the whole interval of the presumption grid-inductance variation. Also, this selection guarantees the control robustness against mismatches of the LCL-filter capacitance and inductance. The real-time computation of advanced controllers is a challenging issue. The computation burden of the proposed CCS-MPC is mostly performed offline and just some simple numerical expression is executed in real time. Thus, it does not require a powerful but expensive processor for implementation. The simulation and experimental results prove the performance of the proposed controller for handling the LCL-filter resonance, grid-inductance variations, and tracking sinusoidal references.