Inthispaper,firstintroduceanddefineanintuitionisticMengerinnerproductspace,andthen,obtainanewfixedpointtheoreminacompleteintuitionisticMengerinnerproductspace.Asanapplication,theresultsareusedtostudytheexistenceanduniquenessofthesolutiontoalinearVolterraintegralequation.