The Collaborative International Dictionary of English v.0.48:

Linnet \Lin"net\ (l[i^]n"n[e^]t), n. [F. linot, linotte, from L.
   linum flax; or perh. shortened from AS. l[imac]netwige, fr.
   AS. l[imac]n flax; -- so called because it feeds on the seeds
   of flax and hemp. See Linen.] (Zool.)
   Any one of several species of fringilline birds of the genera
   Linota, Acanthis, and allied genera, esp. the common
   European species (Linota cannabina), which, in full summer
   plumage, is chestnut brown above, with the breast more or
   less crimson. The feathers of its head are grayish brown,
   tipped with crimson. Called also gray linnet, red linnet,
   rose linnet, brown linnet, lintie, lintwhite, gorse
   thatcher, linnet finch, and greater redpoll. The
   American redpoll linnet (Acanthis linaria) often has the
   crown and throat rosy. See Redpoll, and Twite.
   [1913 Webster]

   Green linnet (Zool.), the European green finch.
      [1913 Webster]

WordNet (r) 3.0 (2006):

linnet
    n 1: small finch originally of the western United States and
         Mexico [syn: house finch, linnet, Carpodacus
         mexicanus]
    2: small Old World finch whose male has a red breast and
       forehead [syn: linnet, lintwhite, Carduelis cannabina]