Quantum batteries (QBs) are emerging quantum energy-storage devices that exploit quantum mechanical principles to store and extract energy, and achieving efficient charging is one of the central issues in current quantum battery research. In this work, we investigate a Fermi-Hubbard quantum battery and employ a variational superadiabatic protocol to construct an approximate adiabatic gauge potential, which is introduced into the system Hamiltonian as a counterdiabatic correction term to optimize the charging process. To avoid the difficulties associated with constructing the exact adiabatic gauge potential in a many-body system, we adopt a nested-commutator expansion to construct an approximate adiabatic gauge potential and determine the corresponding variational coefficients by minimizing the Hilbert-Schmidt action. Counterdiabatic correction terms with different expansion orders are then constructed, and their effects on the charging performance of the quantum battery are compared. By solving the dynamical evolution of the system, we systematically analyze the stored energy, average charging power, quantum fluctuation of energy, and fidelity, both with and without the counterdiabatic term. We further explore the effects of the interaction strength, evolution time, and system size on the charging performance. The results show that the counterdiabatic term effectively suppresses nonadiabatic transitions induced during finite-time evolution, significantly enhances the stored energy and average charging power, reduces the quantum fluctuation of energy, and maintains a high final fidelity. Increasing the expansion order further improves the charging performance, particularly in the regime of strong interactions and short charging times. The optimization remains effective for different particle numbers, indicating its applicability to Fermi-Hubbard quantum batteries of different system sizes. This work provides a feasible theoretical approach to the high-efficiency charging and optimal control of many-body QBs and may offer useful guidance for quantum energy-storage devices based on ultracold atomic systems.