Grid-forming　control　has　been　recognized　as　a　flexible　and　robust　solution　for　wind　turbine　(WT)　integrating　into　weak　AC　grid　in　the　research　community.　This　paper　investigates　the　damping　properties　of　the　grid-forming　permanent　magnet　synchronous　generator　(PMSG)-based　WT　under　different　reactive　power　oscillation　damping　controls.　First,　a　recently　developed　grid-forming　control,　namely,　the　DC　voltage　synchronization　control　(DVSC),　is　implemented　in　PMSG-based　WT,　enabling　WT　with　capabilities　of　inertial　response　and　grid-synchronization　without　the　phase-　locked　loop　(PLL).　Then,　two　different　reactive　power　controls,　i.e.,　the　convert　er　voltage　control　and　the　reactive　power　droop　control,　are　further　designed　with　corresponding　damping　controllers.　Moreover,　the　impacts　of　associated　control　parameters　and　operating　conditions　on　system　damping　characteristics　are　substantially　and　analytically　evaluated,　which　can　provide　guidance　for　parameter　tuning.　The　proposed　damping　controls　stand　out　by:　1)　fully　utilizing　the　capacity　of　the　converter　and　the　reserved　energy　in　DC　capacitor　to　contribute　to　system　damping　support,　2)　not　impairing　maximum　power　point　track　(MPPT)　status　of　WT.　Case　studies　are　conducted　under　several　power　system　contingencies　to　validate　the　effectiveness　of　the　proposed　damping　control.　©　2022　IEEE.