Abstract: A quickest detection method related to a step function was proposed. Firstly, a probability model was established, making the priori probability of a change point be switched with current states. Then a Bayesian quickest detection rule was established based on the optimal stopping theory. Finally, computer simulation was carried out, analyzing the probability of false alarm and the mean time of delay. Simulation results show the validity of the method. This method can introduce Bayesian quickest detection theory into more application area.