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Voice conversion technique, which modifies one speaker's (source) voice to sound like another speaker (target), presents a threat to automatic speaker verification. In this paper, we first present new results of evaluating the vulnerability of current state-of-the-art speaker verification systems: Gaussian mixture model with joint factor analysis (GMM-JFA) and probabilistic linear discriminant analysis (PLDA) systems, against spoofing attacks. The spoofing attacks are simulated by two voice conversion techniques: Gaussian mixture model based conversion and unit selection based conversion. To reduce false acceptance rate caused by spoofing attack, we propose a general anti-spoofing attack framework for the speaker verification systems, where a converted speech detector is adopted as a post-processing module for the speaker verification system's acceptance decision. The detector decides whether the accepted claim is human speech or converted speech. A subset of the core task in the NIST SRE 2006 corpus is used to evaluate the vulnerability of speaker verification system and the performance of converted speech detector. The results indicate that both conversion techniques can increase the false acceptance rate of GMM-JFA and PLDA system, while the converted speech detector can reduce the false acceptance rate from 31.54% and 41.25% to 1.64% and 1.71% for GMM-JFA and PLDA system on unit-selection based converted speech, respectively.