Global climate change interacts in complex ways with biological invasions, yet the mechanisms enabling invasive species to maintain adaptive capacity under changing conditions remain poorly understood. In particular, the relative and interactive roles of genetic and epigenetic variations in mediating environmental adaptation, and their joint influence on future invasion risks, are unresolved. Here, we integrated population (epi)genomics and predictive modeling to investigate the molecular basis of environmental adaptation in the globally invasive ascidian Molgula manhattensis. Using the genomic and methylomic sequencing across five populations along the Chinese coastline, we detected strong north-south population divergence at both genetic and epigenetic levels, accompanied by extensive environment-associated genomic and epigenomic variations. Mantel tests and methylation quantitative trait locus (mQTL) analyses revealed weak genomic-epigenomic coupling, with genetic variation explaining only 34.42 % of environment-associated methylation variation, indicating largely autonomous epigenetic regulation. Functional analyses showed that genetic and epigenetic variations were linked to both overlapping and unique sets of genes and biological pathways, suggesting functional complementarity between the two layers of variations. Generalized dissimilarity modeling further revealed pronounced spatial heterogeneity in genomic and epigenomic offsets, with southern populations exhibiting lower offsets and thus potentially greater adaptive potential and higher invasion risks than northern populations under future climate scenarios. Collectively, this study advances our mechanistic understanding of invasion dynamics and underscores the importance of incorporating multi-omics information into frameworks for predicting invasion risks and managing biological invasions under global climate change.