In order to effectively recognize the failure behaviour of the diesel particulate filter (DPF), a failure cusp catastrophe model of a porous medium filter in DPF was established using catastrophe theory and diffeomorphism transformation based on the flow resistance model of a porous medium filter with ash deposition. Then, critical points and singular points of the failure cusp catastrophe model were solved and the discriminant of the DPF failure cusp catastrophic model was obtained, which was used to recognize the failure behaviour of the DPF. Finally, failure or critical state details of DPF were acquired via calculation examples, and recognition results of the DPF failure behaviour were verified on the engine bench test. Recognition results of the failure state are consistent with the experimental ones, which confirms the validity of failure recognition based on the failure cusp catastrophe model of DPF, and provides a theoretical basis and reference for research on the failure prediction and diagnosis, as well as the anti-failure, of DPF.