Genetic diversity is important for species' fitness and evolutionary processes but our knowledge on how it varies across a species' distribution range is limited. The abundant centre hypothesis (ACH) predicts that populations become smaller and more isolated towards the geographic range periphery - a pattern that in turn should be associated with decreasing genetic diversity and increasing genetic differentiation. We tested this hypothesis in Adonis vernalis, a dry grassland plant with an extensive Eurasian distribution. Its life-history traits and distribution characteristics suggest a low genetic diversity that decreases and a high genetic differentiation that increases towards the range edge. We analysed AFLP fingerprints in 28 populations along a 4698-km transect from the geographic range core in Russia to the western range periphery in Central and Western Europe. Contrary to our expectation, our analysis revealed high genetic diversity (range of proportion of polymorphic bands = 56-81%, He = 0.168-0.238) and low genetic differentiation across populations (Φ(ST) = 0.18). However, in congruence with the genetic predictions of the ACH, genetic diversity decreased and genetic differentiation increased towards the range periphery. Spanish populations were genetically distinct, suggesting a divergent post-glacial history in this region. The high genetic diversity and low genetic differentiation in the remaining A. vernalis populations is surprising given the species' life-history traits and points to the possibility that the species has been widely distributed in the studied region or that it has migrated from a diverse source in an East-West direction, in the past.