A search for Higgs boson pair (HH) production in association with a vector boson V (W or Z boson) is presented. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV, collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb−1. Both hadronic and leptonic decays of V bosons are used. The leptons considered are electrons, muons, and neutrinos. The HH production is searched for in the bb¯bb¯ decay channel. An observed (expected) upper limit at 95% confidence level of VHH production cross section is set at 294 (124) times the standard model prediction. Constraints are also set on the modifiers of the Higgs boson trilinear self-coupling, kλ, assuming k2V = 1, and vice versa on the coupling of two Higgs bosons with two vector bosons, k2V. The observed (expected) 95% confidence intervals of these coupling modifiers are −37.7 < kλ < 37.2 (−30.1 < kλ < 28.9) and −12.2 < k2V < 13.5 (−7.2 < k2V < 8.9), respectively.