Study of coal oxidation at low temperatures forms the basis of investigating the inherent properties of spontaneous combustion of coal. In general, the process of coal oxidation at low temperatures is very complex, involving many factors. Experiments examining the properties of oxidation and ignition of coal have been carried out. Based upon the results of these experiments, the catastrophe properties in the process of coal oxidation are analysed and the mechanism of catastrophe is proved for the ignition of coal. A folding catastrophe model is also established for the process of coal oxidation. Results obtained show that the process of coal oxidation to ignition is discontinuous, where the coal-environment system yields structure destabilisation. The system can jump from one stable attractor to another. The research results presented in this paper help to show the irregularities of coal oxidation at low temperatures and how to pursue effective control measures.