Presented paper with the title ,,European Union Asylum Policy” has the aim to elucidate the history background that preceded the establishment of a common EU asylum policy, such as pre-Amsterdam period. Furthermore, it was addressed the issue regarding legal framework and institutional level responsible for management of EU asylum policy. We presented the means of cooperation between the EU state members with a distinctive policy in the field of asylum. In conclusion we approached to the national legal framework in the field of asylum and we assessed the degree of conformity of the asylum in the Legislation of the Republic of Moldova in relation with the European Union.