We search for electron anti-neutrinos (v̅ₑ) from long- and short-duration gamma-ray bursts (GRBs) using data taken by the Kamioka Liquid Scintillator Anti-Neutrino Detector (KamLAND) from 2002 August to 2013 June. No statistically significant excess over the background level is found. We place the tightest upper limits on v̅ₑ fluence from GRBs below 7 MeV and place first constraints on the relation between v̅ₑ luminosity and effective temperature.