The reliable operation of doubly-fed induction generator (DFIG) wind turbine (WT) systems rely on the accurate information of states. However, due to the unavailability of some states from phasor measurement units (PMUs), dynamic state estimation (DSE) for DFIG-WT connecting to the power system becomes essential. Although various DSEs have been applied, the variable stochastic wind speed was excluded into consideration, leading to the inaccurate estimation results. This paper develops the DSE using centralized Kalman filter (CKF) for DFIG-WT under the stochastic wind speed. The wind speed is modeled by stochastic differential equations (SDE), which can generate the trajectories with statistical properties similar to the wind speed historical data available for a particular location, so that the variable wind speed can be applied to the filtering process. Finally, the system involving a DFIG connected to a standard IEEE 14-bus system is utilized to verify the feasibility of the proposed method with the occurrence of electric faults.