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The chameleon model was proposed as a promising candidate for the dark energy screening mechanism. It is not straightforward to detect the fifth force mediated by the chameleon scalar field in a high-density environment, such as those in a ground-based laboratory. Nevertheless, short-range gravitational experiments such as the torsion pendulum experiment can provide strong constraints on the chameleon model. In this work, we constrain the chameleon model from a precise test of the inverse-square law at Huazhong University of Science and Technology. In particular, we take full advantage of the regular flat-plate structure of the test and attraction mass, which gives rise to accurate modeling for the chameleon force and torque. The derived analytical results on the chameleon torque are shown to agree well with those by numerical calculations. Subsequently, based on the experimental data, the parameter space of the chameleon model is analyzed, and the results are presented in terms of a more stringent constraint on the model parameters. [ABSTRACT FROM AUTHOR]