The Brillouin dynamic grating model is developed based on the stimulated Brillouin scattering and elastic acoustic theory. The reflection spectrum of the Brillouin dynamic grating is calculated based on the fiber Bragg grating theory， and it is demonstrated that the Bragg wavelength downshifts by Brillouin frequency shift equals the Doppler frequency shift. The reflectivity and the spectral width are calculated when the pump power ranges from 0.1 W to 30 W， the pulse width ranges from 2 ns to 10 ns and the core diameter of a single mode fiber ranges from 8 μm to 10 μm. When the power increases to 30 W and the pump pulse width reaches 10 ns， the peak reflectivity is 2.17×10^-6 and 7.16×10^-9， respectively. The spectral width of the reflection spectrum decreases with the increase of pulse width. When the pulse width is 10 ns， the minimum spectral width is 1.2×10^-4 nm. When the fiber core diameter decreases to 8 μm， the peak reflectivity increases to 6.64×10^-11. The results show that the reflectivity of the Brillouin dynamic grating is positive correlation with the power and the pulse width of the pump wave， but it is negative correlation with the core diameter of optical fiber. The spectral width of the reflection spectrum is not affected by the power of the pump wave and the diameter of the fiber core， but it is negative correlation with the pulse width.