Mobile ad-hoc network (MANET) has been focused in the ubiquitous network. MANET is the network configured autonomously by wireless mobile terminals. Many routing protocols of MANET are proposed and three of them are standardized by IETF. However, the usage of these protocols is limited in internal MANET commonly. MANET is also used to complement or coexist with the infrastructure, called hybrid ad-hoc network. In the hybrid ad-hoc network, gateways connect the MANET to the Internet. Mobile terminals should communicate to the gateway stably. Our research goal is to formulate an algorithm to detect the stability of the route from mobile terminals to gateways. Using this algorithm, mobile terminals can select stable route to the gateway and.will keep connecting to the Internet for longer time. In this paper, we describe the approach that the route stability is determined by hop counts of the route between the mobile terminal and the gateway. We investigate the relation between the route stability and the hop count of the route by the simulation.