A search for Higgs boson pair production (HH) associated with a vector boson V (W or Z boson) is presented. The search is based on 138 ${\rm fb}^{-1}$ of proton-proton (pp) collisions at a center-of-mass energy of 13 TeV, collected with the CMS detector at the LHC. The processes in this search include $\rm pp \rightarrow ZHH$ and $\rm pp \rightarrow WHH$ productions. All hadronic decays and leptonic decays of W and Z bosons involving electrons, muons, and neutrinos are utilized. Higgs bosons are searched for in the $b\bar b b\bar b$ channel. An observed (expected) upper limit at 95$\%$ confidence level (CL) is set at 294 (124) times the cross section from the standard model prediction of the $\rm pp \rightarrow VHH$ process. Constraints are also set on the modifier of the Higgs boson trilinear self-coupling $\kappa_\lambda$, and on the coupling $\kappa_{\rm VV}$ of two Higgs bosons with two vector bosons. The observed (expected) confidence intervals of these coupling modifiers at 95$\%$ CL are -37.7 < $\kappa_\lambda$ < 37.2 (-30.1 < $\kappa_\lambda$ < 28.9) and -12.2 < $\kappa_{\rm VV}$ < 13.5 (-7.64 < $\kappa_{\rm VV}$ < 8.90). In addition, a 95$\%$ CL upper limit is set at 43 (22) times the cross section of the $\rm pp \rightarrow VHH$ process when $\kappa_\lambda$ = 5.5 and other couplings are set to standard model predictions.