We study the experimental constraints on a model of a two-component dark matter, consisting of the QCD axion, and a scalar particle, both contributing to the dark matter relic abundance of the Universe. The global Peccei-Quinn symmetry of the theory can be spontaneously broken down to a residual Z2 symmetry, thereby identifying this scalar as a stable weakly interacting massive particle, i.e., a dark matter candidate, in addition to the axion. We perform a comprehensive study of the model using the latest data from dark matter direct and indirect detection experiments, as well as new physics searches at the Large Hadron Collider. We find that although the model is mostly constrained by the dark matter detection experiments, it is still viable around a small region of the parameter space where the scalar dark matter is half as heavy as the Standard Model Higgs. In this allowed region, the bounds from these experiments are evaded due to a cancellation mechanism in the dark matter-Higgs coupling. The collider search results, however, are shown to impose weak bounds on the model.