To reduce the energy loss and the wearing of a refractory by lowering steel tapping temp. of a converter in the first operation of a continuous casting to the min. limit in the necessary temp.

High temp. inert gas is continuously supplied into a tundish while alternately using plural heat-storage type preheaters. Then, the temp. lowering of the tundish under waiting and heat-holding is stabilized by adopting the non-oxidizing heat-holding method for holding the heat of the tundish under non-oxidizing. This tundish temp. at the time of tapping the molten steel is accurately estimated with an approximate expression containing a function of the heat-holding time while using the last casting molten steel temp. at the previous heat as an initial value, and the steel tapping temp. at this heat is set under consideration of the temp. lowering degree, etc., at the time of pouring the molten steel into this tundish. Further, in the case of starting heat-holding of the tundish after some interval since starting of the waiting, the tundish temp. lowered during no heat-holding is estimated with a different approximate expression and while using this estimated value as an initial value, the tundish temp. during heat-holding is estimated.