Quantum Key Distribution (QKD) technology, based on the laws of physics, can create unconditional security keys between communication parties. In recent years, researchers draw more and more attention to the QKD technology. Privacy amplification is a very significant procedure in QKD system. In this paper, we propose the real-time privacy amplification (RTPA) scheme which converts the weak secret string to a uniform key that is fully secret from Eve. Our detailed proofs show the security of our RTPA scheme. In order to prevent the potential man-in-middle attacks, we employ an authentication procedure to RTPA scheme (ARTPA) with the "-XOR almost universal hash functions. We implement our ARTPA scheme based on CLIP system, which is connected to the quantum communication system. Considering the privacy amplification and authentication overhead and the finite size effect on the security of final keys, we set the secret key length be 256k before privacy amplification and the authentication tag length be 60. Our experimental results show the efficiency of the proposed ARTPA scheme.