Linear and gapless energy spectrum of graphene carriers enables population inversion under optical and electrical pumping. We first theoretically discovered this phenomenon and demonstrated experimental observation of single-mode THz lasing with rather weak intensity at 100K in current-injection pumped graphene-channel field-effect transistors (GFETs). We introduce graphene surface plasmon polariton (SPP) instability to substantially boost the THz gain. We demonstrate our experimental observation of giant amplification of THz radiation at 300K stimulated by graphene plasmon instabilities in asymmetric dual-grating gate (ADGG) GFETs. Integrating the graphene SPP amplifier into a GFET laser will be a promising solution towards room-temperature intense THz lasing.