The　analytic　function　of　relativistic　nonextensive　distribution　is　given,　and　employed　to　solve　the　Landau　damping　of　longitudinal　oscillation　in　ultra-relativistic　plasmas.　The　unified　expression　of　Landau　damping　which　reduces　to　the　result　in　relativistic　Maxwellian　distributed　plasmas　in　the　extensive　limit　is　obtained,　and　find　that　Landau　damping　is　relevant　to　both　the　number　and　energy　of　resonant　particles,　which　described　by　temperature　and　nonextensive　parameters　in　relativistic　nonextensive　distribution.