Satellite networks are booming to provide high-speed and low latency Internet access, but the transport layer becomes one of the main obstacles. Legacy end-to-end TCP is designed for terrestrial networks, not suitable for error-prone, propagation delay varying, and intermittent satellite links. It is necessary to make a clean-slate design for the satellite transport layer. This paper introduces a novel Information-centric Hop-by-Hop transport layer design, INTCP. It carries out hop-by-hop packets retransmission and hop-by-hop congestion control with the help of cache and request-response model. Hop-by-hop retransmission recovers lost packets on hop, reduces retransmission delay. INTCP controls traffic and congestion also by hop. Each hop tries its best to maximize its bandwidth utilization and improves end-to-end throughput. The capability of caching enables asynchronous multicast in transport layer. This would save precious spectrum resources in the satellite network. The performance of INTCP is evaluated with the simulated Starlink constellation. Long-distance communication with more than 1000km is carried out. The results demonstrate that, for the unicast scenario INTCP could reduce 42% one-way delay, 53% delay jitters, and improve 60% throughput compared with the legacy TCP. In multicast scenario, INTCP could achieve more than 6X throughput.