布朗运动是非平衡态统计物理中最基础的课题，但是目前国内大部分教材对这部分内容的处理存在着不当之处，即用坐标乘以朗之万方程两边后求系综平均，引入仅适合平衡态下的能量均分定理，计算自由粒子的暂态方均位移.这种方法给出的表达式是不严格的，对初始时间粒子呈现弹道扩散的解释亦是不正确的.本文基于线性朗之万方程的精确解，得到了布朗粒子速度和坐标二次矩的表达式，并且改进了教材中的矩方法，使之也能获得粒子方均位移的正确结果.

The Brownian motion is a basis subject in non-equilibrium statistical physics. However，the current textbooks have inappropriate problems for explaining this subject，namely，by using the particle's coordinate to multiply the Langevin equation and then averaging over the two sides of the equation，thus the time-dependent mean squared displacement of the force-free particle is calculated. We think that the expression proposed by the moment method of this kind is not rigorous and the explanation for the mechanism of ballistic diffusion motion is also incorrect. Based on the accurate solution of the linear Langevin equation，this paper proposes the expressions of variances of velocity and coordinate of the particle. We also modify the moment method used in the present textbooks and make it give the correct result of the mean squared displacement of the force-free particle.