The Collaborative International Dictionary of English v.0.48:

Anxiousness \Anx"ious*ness\, n.
   The quality of being anxious; great solicitude; anxiety.
   [1913 Webster]

WordNet (r) 3.0 (2006):

anxiousness
    n 1: (psychiatry) a relatively permanent state of worry and
         nervousness occurring in a variety of mental disorders,
         usually accompanied by compulsive behavior or attacks of
         panic [syn: anxiety, anxiousness]
    2: a feeling of mild anxiety about possible developments [syn:
       anxiousness, disquiet]