Characterizing how viruses evolve expands our understanding of the underlying fundamental processes, such as mutation, selection and drift. One group of viruses whose evolution has not yet been extensively studied are the Phycodnaviridae, a globally abundant family of aquatic large dsDNA viruses. Here we studied the evolutionary change of Paramecium bursaria Chlorella Virus 1 (PBCV-1) during experimental coevolution with its algal host. We used pooled genome sequencing of six independently evolved populations to characterize genomic change over five time points. Across six experimental replicates involving either strong or weak demographic fluctuations, we found single nucleotide polymorphisms (SNPs) at 67 sites. The occurrence of genetic variants was highly repeatable, with just two of the SNPs found in only a single experimental replicate. Three genes A122/123R, A140/145R and A540L showed an excess of variable sites, providing new information about potential targets of selection during Chlorella-Chlorovirus coevolution. Our data indicated that the studied populations were not mutation-limited and experienced strong positive selection. Our investigation highlighted relevant processes governing the evolution of aquatic large dsDNA viruses, which ultimately contributes to a better understanding of the functioning of natural aquatic ecosystems.