Accurate wind speed prediction has been becoming an indispensable technology in system security, wind energy utilization, and power grid dispatching in recent years. However, it is an arduous task to predict wind speed due to its variable and random characteristics. For the objective to enhance the performance of forecasting short-term wind speed, this work puts forward a hybrid deep learning model mixing time series decomposition algorithm and gated recurrent unit (GRU). The time series decomposition algorithm combines the following two parts: (1) the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and (2) wavelet packet decomposition (WPD). Firstly, the normalized wind speed time series (WSTS) are handled by CEEMDAN to gain pure fixed-frequency components and a residual signal. The WPD algorithm conducts the second-order decomposition to the first component that contains complex and high frequency signal of raw WSTS. Finally, GRU networks are established for all the relevant components of the signals, and the predicted wind speeds are obtained by superimposing the prediction of each component. Results from two case studies, adopting wind data from laboratory and wind farm, respectively, suggest that the related trend of the WSTS can be separated effectively by the proposed time series decomposition algorithm, and the accuracy of short-time wind speed prediction can be heightened significantly mixing the time series decomposition algorithm and GRU networks.