This paper studies the integrated mobile ad-hoc networks (MANETs) and Internet network which the Mobile IP and AODV routing protocols are integrated to offer MANET nodes to set up multi-hop routes to the Internet. Gateways act as bridges for forwarding data packets between integrated MANETs and the Internet. Mobile nodes in MANETs must discover available gateways to gain access to the Internet. This study presents an adaptive gateway discovery scheme that balances efficiency and overhead by limiting the flooding scope of gateway advertisement messages. The proposed scheme dynamically adjusts the ADV_TTL according to the average delay time of network. The simulation results showed that the proposed scheme obtains the shortest average delay time while keeping the network a relatively lower overhead.