Modelling virulence evolution of multihost parasites in heterogeneous host systems requires knowledge of the parasite biology over its various hosts. We modelled the evolution of virulence of a generalist plant virus, Cucumber mosaic virus (CMV) over two hosts, in which CMV genotypes differ for within-host multiplication and virulence. According to knowledge on CMV biology over different hosts, the model allows for inoculum flows between hosts and for host co-infection by competing virus genotypes, competition affecting transmission rates to new hosts. Parameters of within-host multiplication, within-host competition, virulence and transmission were determined experimentally for different CMV genotypes in each host. Emergence of highly virulent genotypes was predicted to occur as mixed infections, favoured by high vector densities. For most simulated conditions, evolution to high virulence in the more competent Host 1 was little dependent on inoculum flow from Host 2, while in Host 2, it depended on transmission from Host 1. Virulence evolution bifurcated in each host at low, but not at high, vector densities. There was no evidence of between-host trade-offs in CMV life-history traits, at odds with most theoretical assumptions. Predictions agreed with field observations and are relevant for designing control strategies for multihost plant viruses.