Based on a recent experimental data of elastic transmissivity and the elastic reflectivity measured on graphene, we have performed a theoretical study on electron inelastic mean free path (IMFP) and elastic mean free path (EMFP) by an improved approximation in a classical electron trajectory framework. A hump feature, which is considered to be owing to the out-of-plane mode of the π + σ plasmon, is clearly shown in our IMFP results of multilayer graphene while it is not seen in that of monolayer graphene. The obtained EMFPs are one order of magnitude greater than previously reported results. This work shows that the classical electron trajectory framework still works for revealing the physics picture of low-energy electron interaction with graphene, even for the transverse direction of monolayer graphene, which is the thinnest material.