  As a most natural realization of the Next-to Minimal Supersymmetry Standard
Model (NMSSM), {\lambda}-SUSY is parameterized by a large {\lambda} around one
and a low tan$\beta$ below 10. In this work, we first scan the parameter space
of {\lambda}-SUSY by considering various experimental constraints, including
the limitation from the Higgs data updated by the ATLAS and CMS collaborations
in the summer of 2014, then we study the properties of the Higgs bosons. We get
two characteristic features of {\lambda}-SUSY in experimentally allowed
parameter space. One is the triple self coupling of the SM-like Higgs boson may
get enhanced by a factor over 10 in comparison with its SM prediction. The
other is the pair production of the SM-like Higgs boson at the LHC may be two
orders larger than its SM prediction. All these features seems to be
unachievable in the Minimal Supersymmetric Standard Model and in the NMSSM with
a low {\lambda}. Moreover, we also find that naturalness plays an important
role in selecting the parameter space of {\lambda}-SUSY, and that the Higgs
$\chi^2$ obtained with the latest data is usually significantly smaller than
before due to the more consistency of the two collaboration measurements.
