To explore how particularities of a cell-virus system affects viral evolution, we formulate a mathematical model of marine bacteriophage evolution. The intrinsic simplicity of real-life phage-bacteria systems allows to have a reasonably simple model. The model constructed in this paper is based upon Beretta-Kuang model of bacteria-phage interaction. Compared to the Beretta-Kuang model, the model assumes the existence of a multitude of viral variants which correspond to continuously distributed phenotypes. It is noteworthy that this model does not include any explicit law or mechanism of evolution; instead it is assumed, in agreement to the principles of Darwinian evolution, that evolution in this system can occur as a result of random mutations and natural selection. Simulations with a leaner fitness landscape (which is chosen for the convenience of demonstration only) show that a pulse-type traveling wave moving towards increasing Darwinian fitness appears in the phenotype space. This implies that the overall fitness of a viral quasispecies steadily increasing in time. That is, the simulations demonstrate that for an uneven fitness landscape random mutations combined with a mechanism of natural selection lead to the Darwinian evolution. It is noteworthy that in this system the speed of propagation of this wave (and hence the rate of evolution) is not constant but varies, depending on the current viral fitness and the abundance of susceptible bacteria.