In this paper security of the quantum key distribution scheme using correlations of continuous variable Einstein- Podolsky- Rosen (EPR) pairs is investigated. A new approach for calculating the secret information rate △I is proposed by using the Shannon information theory. Employing an available parameter F which is associated with the entanglement of the EPR pairs, one can detect easily the eavesdropping. Results show that the proposed scheme is secure against individual beam splitter attack strategy with a proper squeeze parameter.