The obliquities of the terrestrial planets could have undergone large-amplitude fluctuations. Because the obliquity changes affect the latitudinal distribution of solar radiation, they may have played important roles in the climatic evolution of the planets. We have investigated the effects of obliquity changes on the climate of Mars-like planets with CO2 atmosphere by using a one-dimensional energy balance climate model. Our numerical results show that the obliquity changes would result in the drastic changes of atmospheric pressure (climate jumps) by runaway sublimation of permanent CO2 ice. We also found that given a small solar constant and large obliquity, ring-shaped regions with permanent CO2 ice forms at the mid-latitude.