In composite Higgs models the Higgs boson arises as a pseudo-Goldstone boson from a strongly-interacting sector. Fermion mass generation is possible through partial compositeness accompanied by the appearance of new heavy fermionic resonances. The Higgs couplings to the Standard Model (SM) particles and between the Higgs bosons themselves are modified with respect to the SM. Higgs pair production is sensitive to the trilinear Higgs self-coupling but also to anomalous couplings like the novel 2-Higgs-2-fermion coupling emerging in composite Higgs models. The QCD corrections to SM Higgs boson pair production are known to be large. In this paper we compute, in the limit of heavy loop particle masses, the next-to-leading order (NLO) QCD corrections to Higgs pair production in composite Higgs models without and with new heavy fermions. The relative QCD corrections are found to be almost insensitive both to the compositeness of the Higgs boson and to the details of the heavy fermion spectrum, since the leading order cross section dominantly factorizes. With the obtained results we investigate the question if, taking into account Higgs cou ... mehrpling constraints, new physics could first be seen in Higgs pair production. We find this to be the case in the high-luminosity option of the LHC for composite Higgs models with heavy fermions. We also investigate the invariant mass distributions at NLO QCD. While they are sensitive to the Higgs non-linearities and hence anomalous couplings, the influence of the heavy fermions is much less pronounced.