Geostationary Earth Orbit (GEO)-Korea Multi-Purpose Satellite (KOMPSAT)-2B (GK-2B) is a Korean geostationary Earth orbit (GEO) satellite that is scheduled to be launched in 2020 for meteorological and ocean monitoring. While the primary orbit determination (OD) for GK-2B is by ground-based radar observations and the expected orbit precision is less than 1 km, a satellite laser ranging (SLR) technique has been selected as a subsidiary OD method to verify/complement/enhance primary OD results. In general, the available time and equipment for observing GEO satellites with SLR are limited. Furthermore, because the optical sensors mounted on GK-2B may be defected by laser, only a domestic single SLR station would obtain the tracking data. This research presents the mitigation of these drawbacks to improve orbit precision. Observation data generation and the associated OD of GK-2B are performed by considering numerical SLR data analysis on Compass-G1, a Chinese GEO navigation satellite, and Chinese SLR station at Changchun. With the OD performed for two scenarios with the varying number of observations, the 3D position error is 24.01 m when 13 observations per day are obtained, while the error becomes 43.46 m when 9 observations per day are obtained. To verify these results, the OD of Compass-G1 using actual SLR data from Changchun station is performed to yield 31.89 m for 3D error, which is favorable compared with the external precise ephemeris by GeoForschungsZentrum (GFZ) analysis center. Therefore, the OD based on single SLR station is applicable to estimating the orbit within less than 100 m.