Alfalfa mosaic virus (AMV) is an important plant virus causing considerable economic loss to alfalfa production. Knowledge of the evolutionary and demographic history of the pathogen is limited but essential to the development of effective and sustainable pathogen management schemes. In this study, we performed worldwide phylodynamic analyses of AMV based on 154 nucleotide sequences of the coat protein gene, sampled from 1985 to 2020, to understand the epidemiology of this pathogen. Bayesian phylogenetic reconstruction estimates that the crown group of AMV dates back to 1840 (95% credibility interval, 1687–1955). We revealed that AMV continuously evolves at a rate of 4.14 × 10−4 substitutions/site/year (95% credibility interval, 1.04 × 10−4 − 6.68 × 10−4). Our phylogeographic analyses identified multiple migration links between Europe and other regions, implying that Europe played a key role in spreading the virus worldwide. Further analyses showed that the clustering pattern of AMV isolates is significantly correlated to geographic regions, indicating that geography-driven adaptation may be a factor that affects the evolution of AMV. Our findings may be potentially used in the development of effective control strategies for AMV.