A continuous casting method of steel comprising steps of: filling molten steel into a continuous casting mold which is cooled; solidifying the molten steel while the filling to form a cast slab (10, 10a); drawing the cast slab from the mold; and spraying cooling water toward the cast slab, the method further comprising: obtaining a cooling water spray amount W0 [kg/ton-cast slab] with which a solidification completion position where solidification of molten steel in the cast slab is completed is set as a predetermined target position under a condition where a drawing speed V of the cast slab is set to a speed V0 [m/min] in advance of the above steps of filling, solidifying and drawing; and obtaining a cooling water spray amount W1 [kg/ton-cast slab] with which the solidification completion position is set as the target position under a condition where the drawing speed V of the cast slab is set to a speed V1 [m/min] which differs from the speed V0 in advance of the above steps of filling, solidifying and drawing, wherein the cast slab is drawn at the speed V0 while spraying cooling water to the cast slab such that cooling water spray amount W is set to W0 and, thereafter, the drawing speed V of the cast slab is changed to the speed V1 from the speed V0, and the cast slab is drawn at the speed V1 while spraying cooling water to the cast slab such that the cooling water spray amount W is set to W1, and a cooling water spray amount Wt [kg/ton-cast slab] which is an amount W of cooling water to be sprayed to the cast slab during a period until a time t [min] which is obtained by dividing a target length Lt of the cast slab from an exit of the mold to the target position along the casting direction by the drawing speed V0 elapses from a point of time Tc at which the drawing speed V is changed satisfies a following formula orafollowing formula. Wt < W 1 under a condition of V 1 < V 0 Wt > W 1 under a condition of V 1 > V 0 filling molten steel into a continuous casting mold which is cooled; solidifying the molten steel while the filling to form a cast slab (10, 10a); drawing the cast slab from the mold; and spraying cooling water toward the cast slab, the method further comprising: obtaining a cooling water spray amount W0 [kg/ton-cast slab] with which a solidification completion position where solidification of molten steel in the cast slab is completed is set as a predetermined target position under a condition where a drawing speed V of the cast slab is set to a speed V0 [m/min] in advance of the above steps of filling, solidifying and drawing; and obtaining a cooling water spray amount W1 [kg/ton-cast slab] with which the solidification completion position is set as the target position under a condition where the drawing speed V of the cast slab is set to a speed V1 [m/min] which differs from the speed V0 in advance of the above steps of filling, solidifying and drawing, wherein the cast slab is drawn at the speed V0 while spraying cooling water to the cast slab such that cooling water spray amount W is set to W0 and, thereafter, the drawing speed V of the cast slab is changed to the speed V1 from the speed V0, and the cast slab is drawn at the speed V1 while spraying cooling water to the cast slab such that the cooling water spray amount W is set to W1, and a cooling water spray amount Wt [kg/ton-cast slab] which is an amount W of cooling water to be sprayed to the cast slab during a period until a time t [min] which is obtained by dividing a target length Lt of the cast slab from an exit of the mold to the target position along the casting direction by the drawing speed V0 elapses from a point of time Tc at which the drawing speed V is changed satisfies a following formula orafollowing formula. Wt < W 1 under a condition of V 1 < V 0 Wt > W 1 under a condition of V 1 > V 0 obtaining a cooling water spray amount W0 [kg/ton-cast slab] with which a solidification completion position where solidification of molten steel in the cast slab is completed is set as a predetermined target position under a condition where a drawing speed V of the cast slab is set to a speed V0 [m/min] in advance of the above steps of filling, solidifying and drawing; and obtaining a cooling water spray amount W1 [kg/ton-cast slab] with which the solidification completion position is set as the target position under a condition where the drawing speed V of the cast slab is set to a speed V1 [m/min] which differs from the speed V0 in advance of the above steps of filling, solidifying and drawing, wherein the cast slab is drawn at the speed V0 while spraying cooling water to the cast slab such that cooling water spray amount W is set to W0 and, thereafter, the drawing speed V of the cast slab is changed to the speed V1 from the speed V0, and the cast slab is drawn at the speed V1 while spraying cooling water to the cast slab such that the cooling water spray amount W is set to W1, and a cooling water spray amount Wt [kg/ton-cast slab] which is an amount W of cooling water to be sprayed to the cast slab during a period until a time t [min] which is obtained by dividing a target length Lt of the cast slab from an exit of the mold to the target position along the casting direction by the drawing speed V0 elapses from a point of time Tc at which the drawing speed V is changed satisfies a following formula orafollowing formula. Wt < W 1 under a condition of V 1 < V 0 Wt > W 1 under a condition of V 1 > V 0