Robust video hashing is an effective method of copy detection. But most existing schemes do not make effective classifications; thus their copy detection performances are unsatisfactory. To address these problems, we propose a robust video hashing based on deep feature and the quaternion generic Fourier descriptor (QGFD) for copy detection. In the proposed hashing scheme, an entropy-weighted secondary frame is calculated by weighting all frames in a video group via color entropy. Because color entropy can reflect frame color information, the incorporation of color entropy into each frame guarantees the discrimination of the proposed hashing scheme and makes the obtained entropy-weighted secondary frame discriminative. Next, the entropy-weighted secondary frames are used to extract deep features and geometric invariant features. The deep features are extracted from the low-frequency discrete cosine transform (DCT) coefficients of feature maps learned by three Inception modules of GoogLeNet. As the low-frequency DCT coefficients indicate feature map content and are stable, the deep features provide good discrimination and robustness. The geometric invariant features are extracted by QGFD. Because QGFD are geometric invariant, the use of QGFD can improve the robustness of the proposed hashing scheme. Hash is ultimately determined by quantifying and combining deep features and geometric invariant features. Many experiments were performed on open datasets and indicate that the proposed hashing scheme is superior to the evaluated hashing schemes in the task of copy detection and classification.