At present, most automatic speaker verification (ASV) systems are vulnerable to replay spoof attacks. Therefore, this paper proposes a new approach for the detection of audio replay spoof attacks. Here, a segment-based hybrid feature extraction method is used, which includes the Mel-frequency cepstral coefficient (MFCC) features and Constant-Q cepstral coefficients (CQCC) features. Then, hybrid features are trained using a variety of deep learning networks, including DenseNet, LSTM, and DenseNet-LSTM hybrid architectures. Experiments using the DenseNet-LSTM model with mixed features framework achieves the best performance. Compared to the baseline system built on the CQCC and Gaussian mixture model (GMM), the proposed method achieved 64.31% relative improvement.