Linear　Thomson　scattering　of　relativistic　electrons　with　few-cycle　laser　pulses　is　theoretically　analyzed,　and　the　radiated　energy　spectra　of　electrons　show　that　attosecond　x-ray　pulses　can　be　supported.　The　influences　of　the　carrier-envelope　phase　offset　phi(CE)　of　the　incident　laser　pulses　and　of　the　initial　phase　as　the　electrons　enter　the　field,　phi(in),　on　the　radiated　x-ray　pulses　are　studied,　and　the　results　demonstrate　that　a　single　attosecond　pulse　can　be　produced　in　linear　Thomson　scattering　by　using　either　a　single-cycle　laser　pulse　with　fixed　carrier-envelope　phase　offset　phi(CE)=0,　or　a　few-cycle　laser　pulse　with　controlled　initial　phase　at　the　electron　entrance　to　the　field　phi(in).