Under the scenario of a power system with high proportion of renewable energy integration and high power electronic penetration (i.e., a “double-high” power system), grid-following inverters rely on phase-locked loop (PLL) to accurately extract the phase of grid voltage. However, problems such as tracking lag and large phase deviation may occur under complex operating conditions. Meanwhile, the traditional grid-connected control strategy based on proportional-integral (PI) regulators involves tedious parameter tuning, which increases the design difficulty of the controller and makes it difficult to adapt to variations in different grid strengths. To address these issues, a full model predictive control (MPC) strategy for grid-following inverters is proposed by leveraging the nonlinear objective constraint handling capability and fast dynamic response characteristics of MPC. First, an MPC-PLL structure under a discrete control set is established to accurately extract the grid voltage phase. Second, continuous control set-model predictive control (CCS-MPC) is adopted to construct an MPC current loop, which can directly output the optimal switching states through control calculations. Finally, an MPC voltage loop with the control objective of DC-side voltage stabilization is built to provide reliable DC-side support and generate the optimal current reference commands. Simulation and experimental results demonstrate that the proposed full MPC strategy outperforms the traditional PI-based strategy in both the transient and steady-state performance under different operating conditions of weak and strong grids. These results provide a novel reference for the development of control technologies for grid-following inverters and offer theoretical support for the stable operation of large-scale renewable energy grid-connected inverters.