A two-dimensional energy balance climate model has been built to investigate the climate on Mars. The model takes into account the balance among solar radiation, longwave radiation, and energy transmission and can be solved analytically by Legendre polynomials. With the parameters for thermal diffusion and radiation processes being properly specified, the model can simulate a reasonable surface atmospheric temperature distribution but not a very perfect vertical atmospheric temperature distribution compared with numerical results, such as those from the Mars Climate Database. With varying solar radiation in a Martian year, the model can simulate the seasonal variation of the air temperature on Mars. With increasing dust content, the Martian atmosphere gradually warms. However, the warming is insignificant in the cold and warm scenarios, in which the dust mixing ratio varies moderately, whereas the warming is significant in the storm scenario, in which the dust mixing ratio increases dramatically. With an increasing albedo value of either the polar cap or the non-ice region, Mars gradually cools. The mean surface atmospheric temperature decreases moderately with an increasing polar ice albedo, whereas it increases dramatically with an increasing non-ice albedo. This increase occurs because the planetary albedo of the ice regions is smaller than that of the non-ice region.