Protection from spoofing attacks is an essential component of speaker verification systems. This paper proposes a novel approach to detect such attacks by utilizing supervectors derived from spectral magnitude and phase information. Three countermeasures are chosen to represent these important information. To combine different countermeasures, score fusion and an anti-spoofing supervector (ASSV) are used. Experiments conducted on ASVspoof 2015 show that the combination of magnitude and phase information obtains relative 90% improvement in terms of the equal error rate (EER) compared to the best subsystem in the development set. The two systems can also be fused to further improve the performance. In addition to accuracy improvements, the new supervector framework is extensible and allows for a more flexible interface to the back-end classifier design.