A nonfreezing liquid is hermetically enclosed in one or more brine bags of a flexible plastic material. In the case using an existing refrigerator equipped with a freezer compartment, the brine bags are placed in a brine bag receiving vessel adapted to be located in the freezer compartment, and a cooling plate is provided at a location at the uppermost one of the brine bags. In freezing, food to be frozen is inserted between the cooling plate and the brine bags or between the brine bags so that at least the greater part of outer peripheries of the food is surrounded by a low temperature environment to substantially the same extent as immersion of the food in the nonfreezing liquid, thereby substantially realizing the liquid surface contact freezing. In the case of a newly fabricated refrigerator, the brine bags are directly placed in an exclusive freezer compartment and further cold air is forced against the cooling plate, thereby obtaining more complete frozen food. In this manner, according to the invention frozen food of high quality can be obtained for a very short period of time.