In　the　study　of　brain　science,　the　free　energy　principle　and　attention　perception　mechanism　have　been　the　two　of　the　most　critical　findings　during　the　past　few　decades,　arousing　a　wide　range　of　attention　and　valuable　applications　from　the　research　fields　of　image　and　video　processing,　computer　vision,　etc.　Motivated　by　the　aforementioned　two　important　findings,　we　in　this　paper　develop　a　brain-inspired　computational　model　for　extremely　few　reference　image　quality　assessment　(IQA),　dubbed　as　BCM.　The　proposed　BCM　implements　with　the　two　main　steps.　First,　we　combine　free　energy　principle　and　sparse　perception　mechanism　to　achieve　the　goal　of　only　using　extremely　few　reference　for　assessing　the　image　quality.　Second,　we　further　introduce　the　attention　perception　mechanism　to　boost　the　assessment　performance　by　improving　the　sparse　perception　mechanism　mentioned　above.　Based　on　the　most　commonly　used　image　quality　database,　it　was　found　that　our　proposed　model　has　derived　higher　performance　than　the　peer　extremely　few　reference　IQA　models　and　competitive　performance　as　compared　with　the　benchmark　full　reference　IQA　models.