The Glauber-type stochastic dynamic interpreted by the mean-field theory has been applied to investigate the dynamic magnetic properties of the Sr2FeMoO6 type double perovskite structure under the time varying magnetic field. First, we used the Glauber dynamics to obtain the dynamic mean-field equations. The time varying average Fe and Mo magnetizations are examined to find the phase region of the system. The dynamic Fe and Mo magnetizations, hysteresis loop areas and correlations are calculated depending on the temperature in order to determine the nature of the first and second order phase transitions, as well as to get the dynamic transition points for different ratio of the system parameters. The dynamic phase diagrams (DPDs) are constructed in the plane of reduced temperature and external magnetic field amplitude (T, h). The DPDs contain paramagnetic (p), ferromagnetic (f), ferrimagnetic-1 (i1), ferrimagnetic-2 (i2) phases and six mixed regions, (f + p), (f + i1), (f + i2), (i1 + p), (i2 + p) and (i1 + i2). The DPDs also exhibit dynamic tricritical points and reentrant phenomena, which strongly depend on interaction parameters.