Abstract: A new risk model is constructed, where the total number of claims satisfies the geometric first-order integer-valued autoregressive process. Moreover, we obtain the equation of the adjustment coefficient. We discuss the relationships among the dependence on the number of claims in each period, the adjustment coefficient, and ruin probability by numerical simulations. The results show that, with the increase of the dependence on the number of claims in each period, the adjustment coefficient decrease and ruin probability increase gradually.