  We have investigated the polarization of attosecond light bursts generated by
nanobunches of electrons from relativistic few-cycle laser pulse interaction
with the surface of overdense plasmas. Particle-in-cell simulation shows that
the polarization state of the generated attosecond burst depends on the
incident-pulse polarization, duration, carrier envelope phase, as well as the
plasma scale length. Through laser and plasma parameter control, without
compromise of generation efficiency, a linearly polarized laser pulse with
azimuth $\theta^i=10^\circ$ can generate an elliptically polarized attosecond
burst with azimuth $|\theta^r_{\rm atto}|\approx61^\circ$ and ellipticity
$\sigma^r_{\rm atto}\approx0.27$; while an elliptically polarized laser pulse
with $\sigma^i\approx0.36$ can generate an almost circularly polarized
attosecond burst with $\sigma^r_{\rm atto}\approx0.95$. The results propose a
new way to a table-top circularly polarized XUV source as a probe with
attosecond scale time resolution for many advanced applications.
