Charged particles with sizes ranging from tens of nanometer to tens of micrometer are created in various situations such as DC discharges, rf discharges, laser-driven plasmas, processing plasmas used in device fabrications, as well as in space such as interstellar clouds, solar system, etc. In general, a large number of background electrons could stick onto the nanoparticle surface during the charging processes and as a result a significant depletion of the electron number density can be encountered. If charged non-spherical nanoparticles are created, they can rotate due to the interaction with surrounding plasmas or oscillating electric field. Therefore, a significant modification of the conventional plasma wave dispersion relations might be necessary for the complex plasma that consists of electrons, ions and nanoparticles. In this work, the growing of dust-acoustic wave is investigated in the presence of the nanoparticles in a superthermal plasma. Full spectrums of the growth rate of the dust-acoustic wave is obtained and analyzed to investigate the effect of nanoparticle rotation. The superthermal plasma effect on the growth rate is also analyzed. The growth rate was found to be enhanced by the rotation of nanoparticles, but suppressed by the superthermal plasmas.