We study the quickest change point detection for systems with multiple possible post-change models. A change point is the time instant at which the distribution of a random process changes. We consider the case that the post-change model is from a finite set of possible models. Under the Bayesian setting, the objective is to minimize the average detection delay (ADD), subject to upper bounds on the probability of false alarm (PFA). The proposed algorithm is a threshold-based sequential test. With asymptotic analysis, the analytical ADD of the proposed algorithm is expressed as closed-form functions of the PFA, prior probabilities of change points and models, and the Kullback-Leibler divergences among various models. The proposed algorithm is shown to be asymptotically optimum in terms of ADD when the PFA tends to zero.