We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=48 μm. This work establishes the strongest bound on the magnitude α of the Yukawa violation in the range of 40-350 μm, and improves the previous bounds by up to a factor of 3 at the length scale λ≈70 μm. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for k=4 and 5.