After propagating through two diffusers (with one moving) placed on the two conjugate planes of an imaging system, a Gaussian beam is modulated randomly to form a dynamic cascade speckle field in the Fresnel zone with respect to the image plane. Both theoretical analysis and experimental results indicate that the linear dependence of the reciprocal of the time-correlation length on the velocity of the moving diffuser is still held in this case. Moreover, the time-space correlation function of the speckle field is more sensitive to the motion of the diffuse than that of single-scattered speckle.