Linear Thomson scattering of a short pulse laser by relativistic electron has been investigated using computer simulations. It is shown that scattering of an intense laser pulse of～33 fs full width at haff maximum, with an electron of γ0 = 10 initial energy, generates an ultrashort, pulsed radiation of 76 attoseconds with a photon wavelength of 2.5 nm in the backward direction. The scattered radiation generated by a highly relativistic electron has superior quality in terms of its pulse width and angular distribution in comparison to the one generated by lower relativistic energy electron.