In synthetic aperture imaging ladar (SAIL), the image quality is seriously degraded by the laser speckle effect. Based on the SAIL system in far-field diffraction region, the physical models of laser speckle effect are established, and the expressions for the intensity of speckles are derived. The reasons of space-time speckle effect are analyzed, and the specific speckle patterns are obtained. Research results indicate the statistical properties by simulating the phase and amplitude distribution of typical space-time speckle patterns. Simulation results show that the average width of speckle pattern equals the scale of footprint in SAIL system. The moving distance of speckle pattern along the range direction during a period of pulse time and the average speckle scale are roughly equivalent. Experiments are conducted on big aperture SAIL. Experimental results confirms the prediction. The vivid space-time speckle effect is firstly demonstrated. Simulation results provide a certain reference to the speckle reduction by using multi-channel transmitter/receiver.