We propose an extension of the Floquet theory for constructing quantum entangling gates in ground-state manifolds of Rydberg atoms. By dynamically controlling periodically modulating the Rabi frequencies of transitions between ground and Rydberg states of atoms, error-resilient two-qubit entangling gates can be implemented in the regime of Rydberg blockade. According to different degrees of Floquet theory utilization, the fidelity of the resulting controlled gates surpasses that of the original reference. Our method only uses encoding in the ground states, and compared to the original scheme using Rydberg state for encoding, it is less susceptible to environmental interference, making it more practical to implement. Therefore, our approach may have broader applications or potential for further expansion of geometric quantum computation with neutral atoms.