Previous studies on stability of the Martian climate system used essentially zero-dimensional energy balance climate models (EBMs) under the condition of annual mean solar radiation income. However, areal extent of polar ice caps should affect the Martian climate through the energy balance and the CO2 budget, and results under the seasonal change condition of solar radiation will be different from those under the annual mean condition. We therefore construct a one-dimensional energy balance climate model with CO2-dependent outgoing radiation, seasonal changes of solar radiation income, changes of areal extent of CO2 ice caps, and adsorption of CO2 by regolith. We have investigated behaviors of the Martian climate system and, in particular, examined the effect of the seasonal changes of solar radiation by comparing the results of previous studies under the condition of annual mean solar radiation. One of the major discrepancies between them is the condition for multiple solutions of the Martian climate system. Although the Martian climate system always has multiple solutions under the annual mean condition, under the seasonal change condition, existence of multiple solutions depends on the present amounts of CO2 in the ice caps and the regolith.