A one-dimensional, time-dependent model has been developed to investigate seasonal variations in ozone density in the Martian atmosphere. The model utilizes data for atmospheric temperature, pressure, and water vapor abundance observed by Viking. The results indicate that a high ozone density is not produced near the winter solstice but is in rather late winter, when the amount of water vapor is still small and the solar radiation can pepentrate more deeply. A similar condition met in early winter does not necessarily produce a high ozone density because of the predicted higher HO2 density. Seasonal variations in ozone abundance are discussed in terms of the abundances of H2O and H2 and the seasonal variations in their reaction products H2O2 and HOx. The roles of transport, the effects of ozone loss to the surface, and the differences between northern and southern hemisphere ozone distributions are also discussed.