Change-point analysis is performed in many fields such as finance, medicine, and macroeconomics. This study mainly considers the change-point problems in p-order regressive models. Using the generalized inverse matrix and maximum likelihood methods under the large sample condition, we obtain the asymptotic distribution of test statistics when the data matrix is not full-rank. We then obtain the asymptotic critical value. In addition, we offer their respective proofs. Simulation results indicate that the method is feasible, and the theoretical results are confirmed.