We present the periods of apsidal motion for 27 early-type eclipsing binaries with high eccentricity located in the Small Magellanic Cloud. New times of minima were derived from the light curves constructed by the MACHO, Optical Gravitational Lensing Experiment (OGLE)-II, and OGLE-III survey data. The eclipse timing diagrams of the binary systems were analyzed using those timings and the elements of apsidal motions were obtained in detail for the first time. The apsidal motion periods of all systems were estimated by detailed analysis of both eclipse timings and light curves; a strong correlation value between both methods is shown. We confirm that OGLE-SMC-ECL-2194 shows the shortest known apsidal motion period of 7.1yr in a detached system with main sequence stars. Nineteen systems show intermediate apsidal motion periods between 10 and 100yr, and seven systems exhibit long apsidal periods of more than 100yr.