A method for preparing transition metal composite hydroxide particles using a reactor having a closed structure comprising: a stationary hollow cylinder; a rotary cylinder having the same axis as the stationary hollow cylinder and an outer diameter smaller than an inner diameter of the stationary hollow cylinder; an electric motor to generate power, enabling rotation of the rotary cylinder; a rotation reaction area disposed between the stationary hollow cylinder and the rotary cylinder, wherein ring-shaped vortex pairs that are uniformly arranged in a rotation axis direction and rotate in opposite directions are formed in the rotation reaction area; and two or more inlets through which a reactant fluid is fed into the rotation reaction area and an outlet through which the reactant fluid is discharged from the rotation reaction area, wherein a ratio of a distance between the stationary hollow cylinder and the rotary cylinder to the outer radius of the rotary cylinder is higher than 0.05 and lower than 0.4, the method comprising: injecting raw materials comprising an aqueous solution of two or more transition metal salts and an aqueous solution of a complex-forming additive, and a basic aqueous solution for maintaining pH of an aqueous solution of the raw materials within a range of 10 to 12, into the rotation reaction area of the reactor through the inlet; and performing coprecipitation reaction under a non-nitrogen atmosphere for 1 to 6 hours, wherein a kinematic viscosity of reactant fluid is 0.4 to 400 cP and power consumed per unit weight thereof is 0.05 to 100 W/kg, wherein a critical Reynolds number of the vortex pairs is 300 or more, and wherein the transition metal composite hydroxide particles prepared has a mean particle size of 1 μ m to 5 μ m. a stationary hollow cylinder; a rotary cylinder having the same axis as the stationary hollow cylinder and an outer diameter smaller than an inner diameter of the stationary hollow cylinder; an electric motor to generate power, enabling rotation of the rotary cylinder; a rotation reaction area disposed between the stationary hollow cylinder and the rotary cylinder, wherein ring-shaped vortex pairs that are uniformly arranged in a rotation axis direction and rotate in opposite directions are formed in the rotation reaction area; and two or more inlets through which a reactant fluid is fed into the rotation reaction area and an outlet through which the reactant fluid is discharged from the rotation reaction area, wherein a ratio of a distance between the stationary hollow cylinder and the rotary cylinder to the outer radius of the rotary cylinder is higher than 0.05 and lower than 0.4, the method comprising: injecting raw materials comprising an aqueous solution of two or more transition metal salts and an aqueous solution of a complex-forming additive, and a basic aqueous solution for maintaining pH of an aqueous solution of the raw materials within a range of 10 to 12, into the rotation reaction area of the reactor through the inlet; and performing coprecipitation reaction under a non-nitrogen atmosphere for 1 to 6 hours, wherein a kinematic viscosity of reactant fluid is 0.4 to 400 cP and power consumed per unit weight thereof is 0.05 to 100 W/kg, wherein a critical Reynolds number of the vortex pairs is 300 or more, and wherein the transition metal composite hydroxide particles prepared has a mean particle size of 1 μ m to 5 μ m. injecting raw materials comprising an aqueous solution of two or more transition metal salts and an aqueous solution of a complex-forming additive, and a basic aqueous solution for maintaining pH of an aqueous solution of the raw materials within a range of 10 to 12, into the rotation reaction area of the reactor through the inlet; and performing coprecipitation reaction under a non-nitrogen atmosphere for 1 to 6 hours, wherein a kinematic viscosity of reactant fluid is 0.4 to 400 cP and power consumed per unit weight thereof is 0.05 to 100 W/kg, wherein a critical Reynolds number of the vortex pairs is 300 or more, and wherein the transition metal composite hydroxide particles prepared has a mean particle size of 1 μ m to 5 μ m.