S-wave velocity (Vs) is a critical petrophysical parameter for reservoir characterization. It is desirable to predict Vs based on conventional logging data, but the logging cost is high. Therefore, a deep hybrid neural network coupling the convolutional neural network (CNN), Stacked gated recurrent unit (SGRU) is proposed to predict the Vs, where the inputs to the model are drill cutting features. In the proposed CNN-SGRU hybrid model, CNN is adopted to capture the spatial features from the input data, and SGRU is used to extract the temporal patterns of variation from both the forward and backward directions. To illustrate the prediction effect, the glutenite reservoir in the Baikouquan Formation of Mahu Sag, Junggar Basin is taken as an example. Mineral and pore information of drill cuttings, including siliciclastic content, clay content, quartz content, and void area ratio is chosen as the input data of the CNN-SGRU hybrid model. Three indices are used to quantitatively evaluate the prediction performance, including Mean absolute percentage error (MAPE), Root mean square error (RMSE), and Mean absolute error (MAE). The results show that the prediction accuracy of the proposed model is higher than that of the Xu-White model, CNN, and GRU. Furthermore, the results indicate that drill cuttings can replace logging data to predict Vs.