We examined light curves of 1138 stars brighter than 18.0mag in the I band and less than a mean magnitude error of 0.1mag in the V band from the Optical Gravitational Lensing Experiment (OGLE)-III eclipsing binary catalogue, and found 90 new binary systems exhibiting apsidal motion. In this study, the samples of apsidal motion stars in the Small Magellanic Cloud (SMC) were increased by a factor of about 3.0 than previously known. In order to determine the period of the apsidal motion for the binaries, we analysed in detail both the light curves and eclipse timings using the MACHO (MAssive Compact Halo Objects) and OGLE photometric data base. For the eclipse timing diagrams of the systems, new times of minimum light were derived from the full light curve combined at intervals of one year from the survey data. The new 90 binaries have apsidal motion periods in the range of 12-897yr. An additional short-term oscillation was detected in four systems (OGLE-SMC-ECL-1634, 1947, 3035, and 4946), which most likely arises from the existence of a third body orbiting each eclipsing binary. Since the systems presented here are based on homogeneous data and have been analysed in the same way, they are suitable for further statistical analysis.