The establishment of a possible connection between neutrino emission and gravitational-wave (GW) bursts is important to our understanding of the physical processes that occur when black holes or neutron stars merge. In the Daya Bay experiment, using the data collected from December 2011 to August 2017, a search was performed for electron-Antineutrino signals that coincided with detected GW events, including GW150914, GW151012, GW151226, GW170104, GW170608, GW170814, and GW170817. We used three time windows of 10, 500, and 1000 s relative to the occurrence of the GW events and a neutrino energy range of 1.8 to 100 MeV to search for correlated neutrino candidates. The detected electron-Antineutrino candidates were consistent with the expected background rates for all the three time windows. Assuming monochromatic spectra, we found upper limits (90% confidence level) of the electron-Antineutrino fluence of (1.13-2.44)×1011 cm-2 at 5 MeV to 8.0×107 cm-2 at 100 MeV for the three time windows. Under the assumption of a Fermi-Dirac spectrum, the upper limits were found to be (5.4-7.0)×109 cm-2 for the three time windows.