  Recently, both ATLAS and CMS collaborations at the CERN Large Hadron Collider
(LHC) have announced their observations of an excess of diphoton events around
the invariant mass of $750~{\rm GeV}$ with a local significance of $3.6\sigma$
and $2.6\sigma$, respectively. In this paper, we interpret the diphoton excess
as the on-shell production of a real singlet scalar in the $pp \to S \to \gamma
\gamma$ channel. To accommodate the observed production rate, we further
introduce a vector-like fermion $F$, which is carrying both color and electric
charges. The viable regions of model parameters are explored for this simple
extension of the Standard Model (SM). Moreover, we revisit the problem of
electroweak vacuum stability in the same scenario, and find that the
requirement for the electroweak vacuum stability up to high energy scales
imposes serious constraints on the Yukawa coupling of the vector-like fermion
and the quartic couplings of the SM Higgs boson and the new singlet scalar.
Consequently, a successful explanation for the diphoton excess and the absolute
stability of electroweak vacuum cannot be achieved simultaneously in this
economical setup.
