Double parton scattering (DPS) is studied at the example of $J/psi$ pair-production in the LHCb and ATLAS experiments of the Large Hadron Collider (LHC) at centre-of-mass energies of $sqrt{S}=$ 7, 8, and 13 TeV. We report theoretical predictions delivered to the LHCb and ATLAS collaborations adjusted for the fiducial volumes of the corresponding measurements during Run I and provide new predictions at 13 TeV collision energy. It is shown that DPS can lead to noticeable contributions in the distributions of longitudinal variables of the di-$J/psi$ system, especially at 13 TeV. The increased DPS rate in double $J/psi$ production at high energies will open up more possibilities for the separation of single parton scattering (SPS) and DPS contributions in future studies.
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