A control method for a continuous casting machine , comprising: a molten steel flow state estimating step of estimating, by on-line real-time system, a flow state of molten steel in a mold by using a physical model of numerical hydrodynamics in consideration of a turbulence model and by using an operation condition of a continuous casting machine , including any one of a casting speed, magnetic flux density of the electromagnetic stirring magnetic field, and a nozzle submerging depth, and by using temperature data on the molten steel in the mold ; a molten steel flow index calculating step of calculating, by on-line real-time system, a molten steel flow index based on the flow state of the molten steel estimated at the molten steel flow state estimating step, the molten steel flow index being a factor of mixing of an impurity into a casting inside the mold , wherein the molten steel flow index is a maximum value of a molten steel surface flow velocity in the mold, or an area of a region where a solidification interface flow velocity is equal to or less than a predetermined value, or a maximum value of molten steel surface turbulence energy, or a speed or a flow state at a surface of the molten steel; and an operation condition controlling step of controlling the operation condition of the continuous casting machine such that the molten steel flow index calculated at the molten steel flow index calculating step is within an appropriate range, wherein the operation condition includes any one of a casting speed, a magnetic flux density of an electromagnetic stirring magnetic field, and a nozzle submerging depth. a molten steel flow state estimating step of estimating, by on-line real-time system, a flow state of molten steel in a mold by using a physical model of numerical hydrodynamics in consideration of a turbulence model and by using an operation condition of a continuous casting machine , including any one of a casting speed, magnetic flux density of the electromagnetic stirring magnetic field, and a nozzle submerging depth, and by using temperature data on the molten steel in the mold ; a molten steel flow index calculating step of calculating, by on-line real-time system, a molten steel flow index based on the flow state of the molten steel estimated at the molten steel flow state estimating step, the molten steel flow index being a factor of mixing of an impurity into a casting inside the mold , wherein the molten steel flow index is a maximum value of a molten steel surface flow velocity in the mold, or an area of a region where a solidification interface flow velocity is equal to or less than a predetermined value, or a maximum value of molten steel surface turbulence energy, or a speed or a flow state at a surface of the molten steel; and an operation condition controlling step of controlling the operation condition of the continuous casting machine such that the molten steel flow index calculated at the molten steel flow index calculating step is within an appropriate range, wherein the operation condition includes any one of a casting speed, a magnetic flux density of an electromagnetic stirring magnetic field, and a nozzle submerging depth. <EOS>