  LHC Run-2 has provided intriguing di-photon signals of a new resonance around
750GeV, which, if not due to statistical fluctuations, must call for new
physics beyond the standard model (SM) at TeV scale. We propose a minimal
extension of the SM with a complex singlet scalar $\mathcal{S}$ and a doublet
of vector-like quarks. The scalar sector respects CP symmetry, with its CP-odd
imaginary component $\chi$ providing a natural dark matter (DM) candidate. The
real component of $\mathcal{S}$ serves as the new resonance (750GeV) and
explains the diphoton excess of the LHC Run-2. The new scalar degrees of
freedom of $\mathcal{S}$ help to stabilize the Higgs vacuum, and can realize
the Higgs inflation around GUT scale, consistent with the current cosmology
observations. We construct two representative samples A and B of our model for
demonstration. We study the mono-jet signals of the DM production from
invisible decays Re$(\mathcal{S}) \to \chi\chi$ at the LHC Run-2. We further
derive the DM relic density bound, and analyze the constraints from direct and
indirect DM detections.
