The　generalized　dispersion　equation　for　longitudinal　oscillation　in　an　unmagnetized,　collisionless　and　isotropic　dusty　plasma　composed　of　nonextensive　distributed　electrons,　ions　and　dust　grains　is　derived　based　on　kinetic　theory.　The　analytical　dispersion　relation　of　dust　acoustic　waves　which　is　related　to　nonextensive　parameters　q(alpha)　(alpha　=　e,　i,　d)　is　obtained.　In　the　limit　q(alpha)　-＞　1,　the　result　based　on　the　Maxwellian　distribution　is　recovered.　Using　the　numerical　method,　we　obtain　the　complete　numerical　dispersion　curve　of　longitudinal　oscillation　which　is　in　good　agreement　with　the　analytical　result　of　dust　acoustic　wave　at　v(Td)　＜＜　v　phi　＜＜　v(Ti)　＜＜　v(Te).