This paper proposes a deterministic quantum key distribution scheme based on Gaussian-modulated continuous variable EPR correlations. This scheme can implement fast and efficient key distribution. The security is guaranteed by continuous variable EPR entanglement correlations produced by nondegenerate optical parametric amplifier. For general beam splitter eavesdropping strategy, the secret information rate△I = I(α,β) - I(α,ε) is calculated in view of Shannon information theory. Finally the security analysis is presented.