The production cross section of inclusive J/ψ pairs in pp collisions at a center-of-mass energy √s = 13 TeV is measured with ALICE. The measurement is performed for J/ψ in the rapidity interval 2.5 < y < 4.0 and for transverse momentum pT > 0. The production cross section of inclusive J/ψ pairs is reported to be 10.3 ± 2.3 (stat.) ± 1.3 (syst.) nb in this kinematic interval. The contribution from nonprompt J/ψ (i.e., originated from beauty-hadron decays) to the inclusive sample is evaluated. The effective double-parton scattering cross section is computed, neglecting the single-parton scattering contribution.