Provided are a cold storage method and a cold storage liquid that are suitable for non-freezing refrigerated storage of human or animal stem cells such as iPS cells or embryos in a non-frozen state. According to an embodiment, the non-freezing refrigerated storage liquid is: a mixture liquid (HTMα, HTMx2c13), in which MEM-alpha (Minimum Essential Medium Eagle (MEM) Alpha Modification) is mixed with a UW solution (UW_sln; BELZER UW (registered trademark) COLD STORAGE SOLUTION), or a modified UW solution (polymer component being changed to PVA), are mixed in a ratio of about 1/1 to 1/2; or a storage liquid having a composition equivalent to the mixture liquid, especially in respect of concentrations of potassium ions and sodium ions. And, arousal period(s) of maintaining a temperature of 30°C to 37°C is inserted at each of two to five days, into a non-freezing refrigerated storage period, which is made at 2°C to 8°C for 2 to 10 days or 4 to 20 days.