Existing interoperability maturity models are fragmented and only cover some interoperability aspects. This paper tentatively proposes a maturity model for enterprise interoperability which is elaborated on the basis of existing ones. It is also consistent to the Enterprise Interoperability Framework currently under the standardization process. After a brief introduction, the paper reviews existing maturity models for interoperability and recalls the basic concepts of the Enterprise Interoperability Framework. Then the proposed maturity model for enterprise interoperability is discussed in details. Metrics for determining maturity levels are presented as well. Finally the last part of the paper gives the conclusions and perspectives for future work.