Recently, both ATLAS and CMS collaborations at the CERN Large Hadron Collider (LHC) announced their observations of an excess of diphoton events around the invariant mass of 750 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 -> S -> gamma gamma channel. To accommodate the observed production rate, we further introduce a vector-like fermion F, which carries 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.