Compression of speckle images is significant to storage reduction of measurement systems. We propose a coder for lossless compression of laser speckle images,which is based on speckle displacement estimation,temporal prediction and the Golomb coding. Firstly,speckle displacements are estimated for each subblock. Next,according to correlation properties of dynamic speckle,we set up the prediction model which predicted current pixels model. Finally,prediction errors are coded by the Golomb coding. Key features of the proposed speckle image coder include the estimation of speckle displacement by digital speckle image correlation method and the prediction modeling based on the extremum of the dynamic speckle correlation function. Experimental results show that the proposed coder provides good improvement in compression coding efficiency of laser speckle images.