The measurement of the Higgs boson self-coupling is important to understand what kind of force makes the Higgs boson acquires a VEV. It is expected that Higgs cubic coupling is measured by Higgs pair production at the LHC and ILC, and the deviations from the SM in the Higgs pair production process can give us a hint of new physics beyond the SM. We consider this process from a general potential that achieves the suitable EW symmetry breaking. As an interesting example, we discuss non-perturbative Higgs model in which a runaway type of potential is used. In the model, the cross sections of pair production can be enhanced compared to the SM. We also discuss the Higgs pair production induced by a non-canonical kinetic term of Higgs field, which will be important for searching the pair production at the ILC.