The invention discloses an energy-storage geothermal heating system for absorbing intermittent energy. The system includes a heat storage device, a peak-shaving plate type heat exchanger, a heating plate type heat exchanger, a heat release plate type heat exchanger, a geothermal water circulating pump, a heat supply hot water circulating pump and a heat release circulating pump. The heat storage device converts the intermittent energy into heat energy and stores the heat energy in a heat storage material. In a heating season, the heat energy in the heat storage material is released in a heat supply hot water pipe network through the heat release circulating pump and the peak-shaving plate type heat exchanger to provide peak-shaving heat energy for a building. In a non-heating season, the heat energy in the heat storage material is released in geothermal water through the heat release circulating pump and the heat release plate type heat exchanger and stored in a geothermal reservoir. The system solves the 'source-load' coupling problems between the intermittent energy and a building heating system, such as cross season storage of unstable intermittent energy, matching with the demand of a stable heat source for building heat supply, gradient utilization of heat, and peak shaving of a heat supply network, and is suitable for all kinds of building heating systems with certain geothermal water resources.