Thomson scattering off a pair (electron-positron) plasma is theoretically investigated in the collisionless and collisional limits respectively. Our calculations show that the power spectrum of the Thomson scattering offa collisionless pair plasma is just proportional to the velocity distribution function of the particles in the plasma. Collective modes in the plasma do not have any effects on the Thomson scattering spectrum because of the correlation between the negatively- and positively-charged particles. In the collisional limit, the power spectrum of the Thomson scattering presents three spikes: two peaks correspond to two contra-propagating sound waves and one peak corresponds to an entropy wave.