First-principles calculations have been applied to investigate low-lying C-32 fullerenes and their noble gas endohedral complexes X@C-32. We find that thermodynamic stabilities of related systems may change to the different extent when the noble gas is encaged, which reveals the selectivity of encapsulation for inert gas on different pristine fullerenes. A non-classical fullerene with D-4d symmetry is predicted as the most stable structure and relative stabilities of its endohedral compounds enhance with the enlargement of inserted rare gas. The fragment including one square adjoined with four hexagons plays a substantial role on specific stabilities of corresponding complexes. (C) 2012 Elsevier B. V. All rights reserved.