The IP-based broadband aeronautical satellite network will provide numerous new applications and services for both airspace system operations and passenger communications. However, the interoperation between a satellite system and the exiting terrestrial Internet infrastructure introduces new challenges. In this thesis, we recommend suitable transport protocols for an aeronautical network supporting Internet and data services via satellite. We study the future IP-based aeronautical satellite hybrid network and focus on the problems that cause dramatically degraded performance of the Transport Protocol. Based on the observation that it is difficult for an end-to-end TCP solution to solve the performance problem effectively, we proposed a new splitting based transport protocol, called Aeronautical Transport Control Protocol (AeroTCP). The main idea of AeroTCP is the fixed window flow control, adaptive congestion control, and super fast error control. Simulation results showed that AeroTCP can achieve high utilization of satellite channel and fairness.