This invention discloses a hydrogenation method of CaCO3 with H2 to produce CaO and a syngas product gas containing H2, CO, CO2 and H2O, preferably with a H2/CO mol ratio close to 2. The method operates by arranging a solids containing CaCO3 and at least CaO (as reverse water gas shift catalyst) in a reactor, heating them to a temperature that depends on operating pressure and feeding H2 to react with them and cause a cooling of the solids while producing a syngas and a solids mixture containing an increased fracstion of CaO. The method operates continuously by cyclically recarbonating the CaO with the CO2 contained in a gas, or by feeding new CaCO3 to the bed of solids and extracting an equimolar quantity of CaO.