Intensive transformation of lowland rainforest into oil palm and rubber monocultures is the most common land-use practice in Sumatra (Indonesia), accompanied by invasion of weeds. In the Jambi province, Centotheca lappacea is one of the most abundant alien grass species in plantations and in jungle rubber (an extensively used agroforest), but largely missing in natural rainforests. Here, we investigated putative genetic differentiation and signatures for adaptation in the introduced area. We studied reproductive mode and ploidy level as putative factors for invasiveness of the species. We sampled 19 populations in oil palm and rubber monocultures and in jungle rubber in two regions (Bukit Duabelas and Harapan). Amplified fragment length polymorphisms (AFLP) revealed a high diversity of individual genotypes and only a weak differentiation among populations (FST = 0.173) and between the two regions (FST = 0.065). There was no significant genetic differentiation between the three land-use systems. The metapopulation of C. lappacea consists of five genetic partitions with high levels of admixture; all partitions appeared in both regions, but with different proportions. Within the Bukit Duabelas region we observed significant isolation-by-distance. Nine AFLP loci (5.3% of all loci) were under natural diversifying selection. All studied populations of C. lappacea were diploid, outcrossing and self-incompatible, without any hints of apomixis. The estimated residence time of c. 100 years coincides with the onset of rubber and oil palm planting in Sumatra. In the colonization process, the species is already in a phase of establishment, which may be enhanced by efficient selection acting on a highly diverse gene pool. In the land-use systems, seed dispersal might be enhanced by adhesive spikelets. At present, the abundance of established populations in intensively managed land-use systems might provide opportunities for rapid dispersal of C. lappacea across rural landscapes in Sumatra, while the invasion potential in rainforest ecosystems appears to be moderate as long as they remain undisturbed.