  Compared with the MSSM or the NMSSM with a low \lambda, \lambda-SUSY theory
with a large \lambda around one has been deemed as a most natural realization
of NMSSM. In this work, we treat the next-to-lightest CP-even Higgs boson as
the SM-like Higgs boson in \lambda-SUSY and study the properties of the Higgs
bosons and the pair production of the SM-like Higgs boson by considering
various experiment constraints. We find that naturalness plays an important
role in selecting the parameter space of \lambda-SUSY. In the most natural
region of parameter space, the triple self coupling of the SM-like Higgs boson
compared with its SM prediction may get enhanced by a factor about 7, and the
most dominant contribution to the Higgs pair production comes from the triple
self coupling of the SM-like Higgs boson and the production rate can be greatly
enhanced, maximally 10 times larger than the SM prediction.
