  We present a self-consistent pseudopotential calculation of surface and
image-potential states on $MgB_2(0001)$ for both $B$-terminated ($B-t$) and
$Mg$-terminated ($Mg-t$) surfaces. We find a variety of very clear surface and
subsurface states as well as resonance image-potential states n=1,2 on both
surfaces. The surface layer DOS at $E_F$ is increased by 55% at $B-t$ and by
90% at the $Mg-t$ surface compared to DOS in the corresponding bulk layers.
