  We perform the threshold resummation for Higgs pair production in the
dominant gluon fusion channel to next-to-next-to-leading logarithmic (NNLL)
accuracy. The calculation includes the matching to the next-to-next-to-leading
order (NNLO) cross section obtained in the heavy top-quark limit, and results
in an increase of the inclusive cross section up to 7% at the LHC with
centre-of-mass energy Ecm=14TeV, for the choice of factorization and
renormalization scales $\mu_F=\mu_R=Q$, being Q the invariant mass of the Higgs
pair system. After the resummation is implemented, we estimate the theoretical
uncertainty from the perturbative expansion to be reduced to about +-5.5%, plus
~10% from finite top-mass effects. The resummed cross section turns out to be
rather independent of the value chosen for the central factorization and
renormalization scales in the usual range (Q/2,Q).
