A bstract We consider a conformal complex singlet extension of the Standard Model with a Higgs portal interaction. The global U(1) symmetry of the complex singlet can be either broken or unbroken and we study each scenario. In the unbroken case, the global U(1) symmetry protects the complex singlet from decaying, leading to an ideal cold dark matter candidate with approximately 100 GeV mass along with a significant proportion of thermal relic dark matter abundance. In the broken case, we have developed a renormalization-scale optimization technique to significantly narrow the parameter space and in some situations, provide unique predictions for all the model’s couplings and masses. We have found there exists a second Higgs boson with a mass of approximately 550 GeV that mixes with the known 125 GeV Higgs with a large mixing angle sin θ ≈ 0.47 consistent with current experimental limits. The imaginary part of the complex singlet in the broken case could provide axion dark matter for a wide range of models. Upon including interactions of the complex scalar with an additional vector-like fermion, we explore the possibility of a diphoton excess in both the unbroken and the broken cases. In the unbroken case, the model can provide a natural explanation for diphoton excess if extra terms are introduced providing extra contributions to the singlet mass. In the broken case, we find a set of coupling solutions that yield a second Higgs boson of mass 720 GeV and an 830 GeV extra vector-like fermion F , which is able to address the 750 GeV LHC diphoton excess. We also provide criteria to determine the symmetry breaking pattern in both the Higgs and hidden sectors.