Mikania micrantha H.B.K. (Asteraceae) is one of the world’s most invasive weeds which has been rapidly expanding in tropical Asia, including China, while its close relative M. cordata, the only Mikania species native to China, shows no harm to the local ecosystems. These two species are very similar in morphology but differ remarkably in several ecological and physiological traits, representing an ideal system for comparative analysis to investigate the genetic basis underlying invasion success. In this study, we performed RNA-sequencing on the invader M. micrantha and its native congener M. cordata in China, to unravel the genetic basis underlying the strong invasiveness of M. micrantha. For a more robust comparison, another non-invasive congener M. cordifolia was also sequenced and compared. A total of 52,179, 55,835, and 52,983 unigenes were obtained for M. micrantha, M. cordata, and M. cordifolia, respectively. Phylogenetic analyses and divergence time dating revealed a relatively recent split between M. micrantha and M. cordata, i.e., approximately 4.81 million years ago (MYA), after their divergence with M. cordifolia (8.70 MYA). Gene ontology classifications, pathway assignments and differential expression analysis revealed higher representation or significant up-regulation of genes associated with photosynthesis, energy metabolism, protein modification and stress response in M. micrantha than in M. cordata or M. cordifolia. Analysis of accelerated evolution and positive selection also suggested the importance of these related genes and processes to the adaptability and invasiveness of M. micrantha. Particularly, most (77 out of 112, i.e. 68.75%) positively selected genes found in M. micrantha could be classified into four groups, i.e., energy acquisition and utilization (10 genes), growth and reproduction (13 genes), protection and repair (34 genes), and signal transduction and expression regulation (20 genes), which may have contributed to the high adaptability of M. micrantha to various new environments and the capability to occupy a wider niche, reflected in its high invasiveness. We characterized the transcriptomes of the invasive species M. micrantha and its non-invasive congeners, M. cordata and M. cordifolia. A comparison of their transcriptomes provided insights into the genetic basis of the high invasiveness of M. micrantha.