adjective (a)

• impossible to satisfy(adj.all)

  Example:
  An insatiable demand for old buildings to restore.
  

  Synonym:
  insatiate, unsatiable
  Antonym:
  satiate, satiated
  

  source: wordnet30
• Not satiable; incapable of being satisfied or appeased; very greedy; as, an insatiable appetite, thirst, or desire.(adjective)

  source: webster1913