Spatial distribution of the beam is an important factor of affecting range indicators for satellite laser altimeter. According to the distribution characteristic of received pulse signal and definition of the received pulse signal′s time-centroid and its variance, the influence models of elliptic Gaussian footprint on range and range error for satellite laser altimeter were built, by modeling theoretically the elliptical Gaussian footprint and the linear target. Based on parameters of Geoscience Laser Altimeter System(GLAS), as for three typical observation target with slope degree and roughness(3°, 1.7 m), (12.5°, 8.9 m) and (28.2°, 14.5 m), the influences of the elliptical Gaussian footprint′s ellipticity and azimuth on the range and range error were discussed systematically with the ways of numerical simulation. The results show that laser range almost has no relation with the elliptical Gaussian footprint′s ellipticity and azimuth, its maximal difference is less than 1 mm. However, laser range error will fluctuate markedly with the elliptical Gaussian footprint′s ellipticity and azimuth, corresponding maximal difference reaches 47.04 cm. The conclusions provide practical application values for hardware design and performance assessment of satellite laser altimeter.