The invention discloses an energy-saving stove core capable of rising temperature quickly and a stove, and relates to the field of household coal stoves, firewood stoves and stove cores. The stove core comprises a shell and an inner container; an inner airway and an outer airway are formed in the inner container; the inner airway is in a gap shape which extends from the bottom to the middle of the stove core; the outer airway is positioned between the inner container and the shell and extends from the bottom to the top of the stove core; the outer airway is communicated with the opening of the stove core through a fire gathering ring at the top of the stove core. The invention also discloses the stove comprising the stove core. According to the energy-saving stove core capable of rising temperature quickly, the combustion performance is improved through the inner airway and the outer airway of the inner container; the air in a combustion chamber is more sufficient through the inner airway; the gas which is not fully combusted can be combusted again at the opening of the stove core through the fire gathering ring. The combustion efficiency of the stove core is greatly improved. The energy-saving stove core capable of rising temperature quickly and the stove also have the characteristics of easiness in ignition and quickness in temperature rising.