We compute the production cross section of a pair of Standard Model Higgs bosons at the LHC at next-to-leading order in QCD, including corrections in inverse powers of the top quark mass. We calculate these power corrections through O(1/Mt8) and study their relevance for phenomenology of the double Higgs production. We find that power corrections are significant, even for moderate values of partonic center-of-mass energies, and that convergence of the 1/Mt expansion can be dramatically improved by factorizing the leading order cross section with full Mt-dependence.