Non-geostationary (NGEO) satellite networks have a series of advantages over terrestrial networks. However, traditional routing algorithms such as the Dijkstra's Shortest Path (DSP) algorithm always lead to some Inter-Satellite Links (ISLs) heavily loaded. To guarantee a better distribution of traffic among satellites, this paper proposes a Fuzzy Satellite Congestion Indicator (FSCI) to estimate congestion status among neighboring satellites. Indeed, a satellite notifies its neighboring satellites of its FSCI. When it is about to get congested, it requests its neighboring satellites to decrease their data forwarding rates by sending them a self status notification signaling message. In response, the neighboring satellites search for less congested paths according to Fuzzy Route Determination. The routing strategy discussed above is Fuzzy Satellite Routing(FSR). This routing algorithm avoids both congestion and packet drops at the satellite. It also ensures a better traffic distribution over the entire satellite constellation. The mechanism of multiple traffic classes is also discussed in FSR. The good performance of FSR, in terms of short end-to-end delay, higher throughput, and lower packet drops, is verified via a set of simulations using the Network Simulator 2 (NS2).