We discuss the modified top quark condensation model proposed in Ref. 54. This construction was inspired by the top-seesaw scenario, in which the extra heavy fermion χ that may be paired with the top quark is added. Besides, this model incorporates the ideas of the little Higgs scenario, in which the 125 GeV scalar particle appears as a pseudo-Goldstone boson. This model admits (in addition to the 125 GeV scalar boson H) the heavier scalar excitation H′. We consider the region of parameters, where its mass is MH′∼ 1TeV, the width of H′ is ΓH′∼ 0.3MH′, while the mass of the heavy fermion is mχ ∼ 1TeV. We find that in this model the value of the cross-section σpp→H′+X→γ+γ+X for s = 13TeV is essentially smaller than the present experimental upper bound. Besides, we find that for the chosen values of parameters there should exist the CP-even scalar boson with mass ≈ 2mχ and very small width. In addition, the model predicts the existence of the extra neutral CP-even scalar boson and the charged scalar boson with masses of the order of 1 TeV.