Numerical approximation of the Boltzmann equation is achallenging problem due to its high-dimensional, nonlocal, and nonlinear col-lision integral. Over the past decade, the Fourier-Galerkin spectral methodhas become a popular deterministic method for solving the Boltzmann equa-tion, manifested by its high accuracy and potential of being further accelerated by the fast Fourier transform. Albeit its practical success, the sta-bility of the method is only recently proved by Filbet, F. & Mouhot, C.in [Trans.Amer.Math.Soc. 363, no. 4 (2011): 1947-1980.] by utilizing the”spreading” property of the collision operator. In this work, we provide anew proof based on a careful L2 estimate of the negative part of the solu-tion. We also discuss the applicability of the result to various initial data,including both continuous and discontinuous functions. This is joint workwith Kunlun Qi and Tong Yang.