Multipath error is a main error source in Global Navigation Satellite System (GNSS) data processing, which cannot be removed by a differential technique because of the strong relationship with the environment around the station. The multipath effect of the code observables is more complex than that of the carrier-phase observables, especially for BeiDou Navigation Satellite System (BDS) geostationary orbit (GEO) satellites. In this contribution, we deeply analyzed the characteristic and effect on the precise data processing of GEO satellite multipath errors based on a large number of permanent GNSS stations. A linear combination of code and carrier-phase observables was used to analyze the characteristics of repeatability for BDS GEO’s multipath. Then, a correction method was proposed to eliminate the multipath error of the GEO code observables, based on wavelet transform. The experiment data were collected at 83 globally distributed stations, from multi-GNSS experiments and national BDS augmentation systems, from days 32 to 66 in 2017. The results show that the systematic multipath variation component of the GEO code observables can be obtained with wavelet transform, which can significantly contribute to correcting the multipath error of GEO satellites. The average root mean square error (RMSE) of the multipath series is decreased by approximately 19.5%, 20.2%, and 7.5% for B1, B2, and B3, respectively. In addition, some experiments, including ionospheric delay extraction and satellite clock estimation, were conducted in simulated real-time mode in order to validate the effect of the correction methods. For the ionospheric delay estimation, the average RMSE of the slant ionospheric delay is reduced by approximately 15.5%. Moreover, the multipath correction can contribute greatly to shortening the convergence time of the satellite clock estimation of the BDS GEO satellites.