A low-carbon steel slab producing method includes: adding Ti to a molten steel decarbonized to have a carbon concentration of 0.05 mass % or less, and subsequently adding at least one of La and Ce to adjust a constitution, and producing a smelted molten steel; and pouring the smelted molten steel into a casting mold via a tundish; wherein at least one of La and Ce in a total amount of 0.2 to 1.2 times an increased amount of oxygen in the smelted molten steel during contained in the tundish is added to the smelted molten steel in the tundish, so as to obtain a steel slab having inclusions which contain oxides of Ti and at least one of La and Ce as chief components, and so as to make a composition of each of the inclusions have a mass ratio of 0.1 to 0.7, in terms of (La2O3+Ce2O3)÷TiOn (n=1˜2).