A new test to detect the change-point in the quasi-autocorrelation coefficient (QAC) structure of a simple linear model with heavy-tailed series was developed. It is more general than previous approaches to the change-point problem in that it allows for the process with innovations in the domain of the attraction of a stable law with index $\kappa (0<\kappa <2)$. Since the existing methods for QAC change detection are not satisfactory, we converted QAC change to mean change through the moving window method, which greatly improved the efficiency. Thus, the aim of this paper was to construct a ratio-typed test based on M-estimation for the testing of mean change. Under regular conditions, the asymptotic distribution under the no change null hypothesis was functional of a Wiener process, not that of a Lévy stable process. The divergent rate under the alternative hypothesis was also given. The simulation results demonstrate that the performances of our proposed tests were outstanding. Finally, the theoretical results were applied to an analysis of daily USD/CNY exchange rates with respect to QAC change.