This paper presents a new algorithm called the adaptive logarithmic increase and adaptive decrease algorithm (A-LIAD), which mainly addresses the Round-Trip Time (RTT) fairness problem in satellite networks with a very high propagation delay as an alternative to the current TCP congestion control algorithm. We defined a new increasing function in the fashion of a logarithm depending on the increasing factor ${alpha}$, which is different from the other logarithmic increase algorithm adopting a fixed value of ${alpha}$ = 2 leading to a binary increase. In A-LIAD, the ${alpha}$ value is derived in the RTT function through the analysis. With the modification of the increasing function applied for the congestion avoidance phase, a hybrid scheme is also presented for the slow start phase. From this hybrid scheme, we can avoid an overshooting problem during a slow start phase even without a SACK option. To verify the feasibility of the algorithm for deployment in a high-speed and long-distance network, several aspects are evaluated through an NS-2 simulation. We performed simulations for intra- and interfairness as well as utilization in different conditions of varying RTT, bandwidth, and PER. From these simulations, we showed that although A-LIAD is not the best in all aspects, it provides a competitive performance in almost all aspects, especially in the start-up and packet loss impact, and thus can be an alternative TCP congestion control algorithm for high BDP networks including a satellite network.