Detection of audio spoofing attacks has become vital for automatic speaker verification systems. Spoofing attacks can be obtained with several ways, such as speech synthesis, voice conversion, replay, and mimicry. Extracting discriminative features from speech data can improve the accuracy of detecting these attacks. In fact, a frame-wise weighted magnitude spectrum is found to be effective to detect replay attacks recently. In this work, discriminative features are obtained in a similar fashion (frame-wise weighting), however, a cosine normalized phase spectrum is used since phase-based features have shown decent performance for the given task. The extracted features are then fed to a convolutional neural network as input. In the experiments ASVspoof 2015 and 2017 databases are used to investigate the proposed system’s spoof detection performance for both synthetic and replay attacks, respectively. The results showed that the proposed approach achieved 34.5% relative decrease in the average EER for ASVspoof 2015 evaluation set, compared to the ordinary cosine normalized phase features. Furthermore, the proposed system outperformed the others at detecting S10 attack type of ASVspoof 2015 database.