With　the　fierce　global　competition　on　satellite　networks,　the　building　of　satellite　constellations　grows　explosively.　Sharply　increasing　on-orbit　data　will　face　the　challenge　of　satellite-ground　data　transmission.　GEO　satellites　become　the　top　choice　for　satellite　data　relay　due　to　their　stable　satellite-ground　link.　Most　existing　spectrum　resource　management　for　GEO　relays　is　equipment-oriented　and　benefit　priority,　which　may　lead　to　a　waste　of　spectrum　resources.　In　this　paper,　we　propose　a　real-time　task-oriented　resource　allocation　strategy　for　GEO　relay　systems.　We　model　the　spectrum　allocation　problem　as　a　distributed　non-cooperative　Stackelberg　game　process.　We　prove　that　when　both　sides　of　the　game　pursue　the　maximization　of　personal　revenue,　the　system　will　enter　a　Nash　equilibrium　state,　whereas　spectrum　resources　are　not　fully　used.　Based　on　the　maximization　of　individual　utilities　(U-prior)　and　spectrum　utilization　(S-prior)　methods,　we　design　an　adaptive　dual-mode　pricing　mode　to　maximize　the　spectrum　resources　within　a　certain　loss　of　revenue.　The　simulation　results　show　that　the　S-prior　and　U-prior　have　better　performance　than　the　baseline　method　and　existing　optimization　methods.　Our　proposed　dual-mode　strategy　is　making　more　throughputs　and　has　less　delay　with　little　loss　of　utility　values　than　that　of　individual　utility　maximization.