Experimental evolution studies offer the possibility to examine whether closely related populations converge versus diverge in phenotype and genotype, when challenged to adapt under identical selection pressures. Human rhinoviruses (RV) are largely responsible for common cold illnesses, but little is known whether different strains of these RNA viruses tend to evolve similarly when cultured on cells in laboratory tissue culture. Here we compared and contrasted evolution of two RV-A serotype strains (RV-1A, RV-1B) grown for ~25 passages on mouse-derived LA-4 cells, expanding on a previous study concerning temperature-dependent innate immunity in mouse-adapted rhinovirus strains. Results showed faster adaptation of the population founded by RV-1B, consistent with classic theory predicting more rapid improvement in populations poorly adapted to their environment. Moreover, we observed increased molecular divergence between the two lineages as they adapted to mouse cells, demonstrated by selection targeting different viral capsid genes and different substitutions in affected viral replication genes, across the two populations. Our findings identify the genetic changes associated with human rhinovirus adaptation to a novel mouse host, which furthers the understanding of loci contributing to RV host jumps in mammals and efforts to develop mice as useful animal models for studying RV infection and pathogenicity.