Abstract: A search for the rare decay of a B-0 or B-s(0) meson into the final state J/psi gamma is performed, using data collected by the LHCb experiment in pp collisions at root s = 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb(-1). The observed number of signal candidates is consistent with a background-only hypothesis. Branching fraction values larger than 1.5 x 10(-6) for the B-0 -> J/psi gamma decay mode are excluded at 90% confidence level. For the B-s(0) -> J/psi gamma decay mode, branching fraction values larger than 7.3 x 10(-6) are excluded at 90% confidence level; this is the first branching fraction limit for this decay.