The search for dynamically screening the coupling between the scalar field and matter in high-density environment is achievable with the symmetron model. The high-accuracy and short-range gravity experiment is proposed to test the symmetron model. In this Letter, the data of the HUST-2020 torsion pendulum experiment testing the inverse-square law at submillimeter range is analyzed to constrain the symmetron model. The results show that the HUST-2020 experiment is uniquely sensitive to probe the symmetron model with a mass scale of μ=7.2×10^{-3} eV, and the self-coupling parameter λ≲105 is excluded at mass scale M=0.3 TeV. Especially, at the dark energy scale μ=2.4×10^{-3} eV, the constraint at M=1.3 TeV is improved by about 10 times the previous constraints on the torsion pendulum experiment.