The production of two prompt [Formula: see text] mesons, each with transverse momenta [Formula: see text] GeV and rapidity [Formula: see text], is studied using a sample of proton-proton collisions at [Formula: see text] TeV, corresponding to an integrated luminosity of 11.4 fb[Formula: see text] collected in 2012 with the ATLAS detector at the LHC. The differential cross-section, assuming unpolarised [Formula: see text] production, is measured as a function of the transverse momentum of the lower-[Formula: see text] [Formula: see text] meson, di-[Formula: see text] [Formula: see text] and mass, the difference in rapidity between the two [Formula: see text] mesons, and the azimuthal angle between the two [Formula: see text] mesons. The fraction of prompt pair events due to double parton scattering is determined by studying kinematic correlations between the two [Formula: see text] mesons. The total and double parton scattering cross-sections are compared with predictions. The effective cross-section of double parton scattering is measured to be [Formula: see text] mb.