In view of the fact that people pay more and more attention to the principle of "getting the position according to the person" and "adapting the person to the position" in person-position matching, a dynamic person-position matching decision method based on hesitant fuzzy numbers is proposed. First, the dynamic person-position matching problem with the hesitant fuzzy numbers is described. Then, according to the hesitant fuzzy evaluation matrices of the positions and the candidates, the expected score matrices of bilateral subjects are calculated. Furthermore, based on the idea of the generalized optimal order method and the dominant correlation and the missing correlation coefficient, the satisfaction mean of both people and positions is calculated. According to the satisfaction mean, the growth satisfaction of each period is obtained, and then the exponential decay formula is used to determine the weights of the growth satisfaction. The dynamic satisfaction of bilateral subjects is calculated by aggregating the initial satisfaction mean and the growth satisfaction. On this basis, a stable person-position matching model considering dynamic satisfaction is established and then is solved to obtain the optimal stable person-position matching scheme. Finally, the feasibility and effectiveness of the proposed method are verified by the example analysis of person-position matching. The main contributions of this article are as follows: an effective calculation method for the missing correlation coefficient is presented; a novel effective calculation method for the dynamic satisfaction is proposed by introducing the correlation parameter to combine the missing correlation with the dominant correlation coefficient; an effective stable person-position matching model considering the dynamic satisfaction is established.