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High bit error rate (BER), long delay, dynamic networking and multi-hop nature of satellite networks can affect the transmission performance of integrated networks, which poses a great challenge to the transmission performance of space-air-ground integrated networks constructed by satellite networks and terrestrial multi-hop networks. In order to improve the transmission rate of heterogeneous converged satellite networks and terrestrial multi-hop networks, this study proposed a scheme applicable to the transmission characteristics. By analyzing the transmission characteristics of satellite networks with long delay and high BER and terrestrial wireless multi-hop networks, the data delivery in the slow start-up phase was improved, and the type of lost data in the congestion avoidance phase was discriminated to enhance the transmission performance of the heterogeneous integrated network. The performance of the proposed scheme was further verified by simulation on OPNET software. Results show that, the proposed scheme not only can effectively reduce the queuing delay of nodes but also can enhance the transmission efficiency of multi-hop network terminals and the data transmission rate in the long delay network environment. With the increase in the number of hops, the transmission rate of the proposed protocol is about twice those of other protocols. Therefore, the proposed scheme can help improve the transmission performance of heterogeneous integrated satellite networks and terrestrial multi-hop networks. [ABSTRACT FROM AUTHOR]