The present invention provides a heat storage and heating apparatus using an air heat source and a water heat source which uses various heat sources to store heat and perform heating and selects various operating modes in accordance with a situation. The heat storage and heating apparatus using an air heat source and a water heat source comprises: a solar heat collection unit a heat storage tank having a pipe laid to exchange a heating medium with the solar heat collection unit a heat exchanger having a pipe laid to exchange a heating medium with the heat storage tank a first heating fan coil unit which has a pipe laid to exchange with the heat storage tank and is installed in an indoor space a first cooling fan coil unit which has a pipe connected to the heat exchanger and is installed in the indoor space a compression unit having a pipe laid in the first cooling fan coil unit and the heat exchanger a second heating fan coil unit which is installed in the indoor space and has a pipe connected to the compression unit an expansion valve positioned between the second heating fan coil unit and the heat exchanger to have a pipe laid in the second heating fan coil unit and the heat exchanger a second cooling fan coil unit installed in an outdoor space and positioned between the expansion valve and the compression unit to have a pipe laid in the expansion valve and the compression unit an indoor temperature sensor installed in the indoor space to measure an indoor temperature and a control unit to perform a heat storage operation to store heat of the indoor space or the outdoor space in the heat storage tank if the indoor temperature is higher than or equal to a preset temperature, and use heat of the heat storage tank to heat the indoor space or operate a heat pump cycle with external air as a heat source to perform a heating operation if the indoor temperature is lower than the preset temperature.COPYRIGHT KIPO 2017본 발명은 다양한 열원을 이용하여 축열 및 난방할 수 있으며, 상황에 맞게 다양한 운전을 선택가능한
