[en] 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 $q_{\mathrm{\alpha <!--\; ??\; -->}}$ ($\mathrm{\alpha <!--\; ??\; -->}=e,i,d$) is obtained. In the limit $q_{\mathrm{\alpha <!--\; ??\; -->}}\to <!--\; ???\; -->1$, 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 $v_{Td}\ll <!--\; ???\; -->v_{\mathrm{\phi <!--\; ??\; -->}}\ll <!--\; ???\; -->v_{Ti}\ll <!--\; ???\; -->v_{Te}$. (paper)