Interactions between alien plants and the newly emerging enemies in introduced ranges may determine plant invasion success. However, little is known about whether herbivory-induced responses are transmitted across vegetative generations of plants, and whether epigenetic changes are involved during this process. In a greenhouse experiment, we examined the effects of current, parental and/or grand-parental herbivory by the generalist herbivore Spodoptera litura on the growth, physiology, and biomass allocation, and the status of DNA methylation of the first-, second- and/or third-generation clonal offspring of the invasive plant Alternanthera philoxeroides, which were derived from two types of root fragments with different branching orders (i.e., the primary- or secondary-root fragments of taproots). Parental herbivory promoted the growth of the second-generation plants sprouted from the secondary-root fragments, but had a neutral or negative effect on the growth of the second-generation plants from the primary-root fragments. The growth of the third-generation plants was significantly reduced by current herbivory, but not affected by grand-parental herbivory. The first-generation plants exhibited a higher level of DNA methylation when they were grazed by herbivores than when they were not, while neither the second-generation nor the third-generation plants showed the herbivory-mediated changes in DNA methylation. Overall, the herbivory-induced growth response within one generation may represent rapid acclimatization of A. philoxeroides to the unpredictable generalist herbivores in the introduced ranges. Herbivory-induced trans-generational effects may be transient for clonal offspring of A. philoxeroides, which can be influenced by the branching order of taproots, but be less characterized by DNA methylation.