The production cross-section of J/psi pairs is measured using a data sample of pp collisions collected by the LHCb experiment at a centre-of-mass energy of root s = 13TeV, corresponding to an integrated luminosity of 279 +/- 11 pb(-1). The measurement is performed for J/psi mesons with a transverse momentum of less than 10 GeV/c in the rapidity range 2.0 < y < 4.5. The production cross-section is measured to be 15.2 +/- 1.0 +/- 0.9 nb. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the J/psi pair are measured and compared to theoretical predictions.