The impacts of random attitude measurement errors on the positioning accuracy of laser footprints and digital surface model (DSM) accuracy of airborne lidar are studied. The principle of airborne lidar is analyzed. The transformation formulas between the random attitude measurement errors and the positioning errors of laser footprints are derived. Three terrains are simulated and the impacts of the random attitude measurement errors on laser point clouds and the corresponding DSM of the three terrains are analyzed. A semi-physical simulation experiment is carried out. The impacts of the random attitude measurement errors on the positioning accuracy of laser footprints and the DSM accuracy are quantitatively evaluated. The simulation and experimental results show that the random attitude measurement errors decrease the accuracy of laser point cloud and DSM. With the parameters used in this research, the horizontal coordinate errors caused by the random attitude measurement errors are about 4～5 times higher of the vertical coordinate error. In addition, when the random attitude measurement errors increase 10 times, the coordinate errors of laser point cloud increase about 10 times, while the error of the DSM increases by about 40 times statistically.