The Geoscience Laser Altimeter System (GLAS) mission is designed to measure changes in the volume and mass of both the Greenland and Antarctic ice sheets. The ICESat satellite will carry the GLAS altimeter, and will have a nominal orbit altitude of 600 km, eccentricity of 0.0013, and orbit inclination of 94 degrees. The groundtrack repeat period is 182 days and will be maintained to within 1 km at the equator via routine orbit adjustments. Science requirements for the GLAS mission demand that the laser altimeter be pointed to within 50 meters, crosstrack, of a defined reference groundtrack. As the actual ICESat groundtrack drifts away from the reference groundtrack, the attitude must be controlled such that the altimeter boresight is pointed at the reference groundtrack, This orientation may be described by a rotation, theta, about the instantaneous local horizontal direction vector, which lies in the orbit plane and is pointed in the direction of motion of the satellite. This paper describes the attitude algorithm required to maintain reference groundtrack pointing. The algorithm was tested for two cases: (I) a maximum equatorial offset of 1 km and (2) a maximum inclination error of 0.03 degrees in addition to the 1 km equatorial offset. Results show that the rotation angle, theta, ranges between +/- 350 arcsecs during a given day for case (1) and +/- 1200 arcsecs during a given day for case (2). The effect of topography on computation of the rotation angle was also studied. Neglecting topography results in rotation angle errors that range between -2 arcsecs and +3 arcsecs for case (1) and -8 arcsecs (23 m crosstrack) to +10 arcsecs (29 m crosstrack) for case (2). Finally, an overview of an automated attitude control system, which includes the corrections due to topography (JGP95E), is discussed.