Identifying single-phase high-entropy alloys (HEAs) is of fundamental importance to understanding HEA formation and their intrinsic properties. However, to date single-phase HEAs are still very limited. Here we present an efficient searching strategy that combines experimental phase diagram inspection, CALPHAD calculations, and first-principles density functional theory modeling. Our research progress in designing new single-phase HEAs in the FCC, BCC and HCP structures in 4-12 component systems will be presented. Thermodynamic analysis as a function of the number of components, composition, and temperatures will be demonstrated. In light of the present research results, HEA formation rules will be discussed.