A method for preparing transition metal composite hydroxide particles using a reactor having a closed structure including: a hollow fixed cylinder; a rotating cylinder having the same axis as that of the hollow fixed cylinder and having an outer diameter that is smaller than an inner diameter of the fixed cylinder; an electric motor to generate power for rotation of the rotating cylinder; a rotating reaction space, as a separation space between the hollow fixed cylinder and the rotating cylinder, in which ring-shaped vortex pairs periodically arranged along a rotating shaft and rotating in opposite directions are formed; and an inlet and an outlet that respectively introduce and discharge a reaction fluid into and from the rotating reaction space, wherein a ratio of a distance between the fixed cylinder and the rotating cylinder to the outer radius of the rotating cylinder is greater than 0.05 and less than 0.4, wherein the reaction fluid has a kinematic viscosity of 0.4 to 400 cP and the reactor has a power consumption per unit mass of 0.05 W/kg to 100 W/kg, wherein the power consumption per unit mass is defined as a stirring rate of the rotating cylinder, and the vortex pairs have a critical Reynolds number of 300, wherein the composite transition metal hydroxide particles are prepared by introducing, into the rotating reaction space of the reactor, an aqueous solution of raw materials including an aqueous solution of at least two transition metal salts and a basic aqueous solution so as to maintain pH of the aqueous solution of raw materials at a constant level of 10 to 12 via the inlet of the reactor and performing co-precipitation thereof in a non-nitrogen atmosphere for 1 to 6 hours, and the composite transition metal hydroxide particles comprising at least two transition metals and having an average diameter of 1 μm to 5 μm, wherein the composite transition metal hydroxide particles exhibit monodisperse particle size distribution and have a coefficient of variation of 0.2 to 0.7, wherein the composite transition metal hydroxide particles contain an impurity derived from a transition metal salt for preparation of a composite transition metal hydroxide, wherein an amount of the impurity is 0.3 wt% to 0.4 wt% based on a total weight of the composite transition metal hydroxide particles. a hollow fixed cylinder; a rotating cylinder having the same axis as that of the hollow fixed cylinder and having an outer diameter that is smaller than an inner diameter of the fixed cylinder; an electric motor to generate power for rotation of the rotating cylinder; a rotating reaction space, as a separation space between the hollow fixed cylinder and the rotating cylinder, in which ring-shaped vortex pairs periodically arranged along a rotating shaft and rotating in opposite directions are formed; and an inlet and an outlet that respectively introduce and discharge a reaction fluid into and from the rotating reaction space, wherein a ratio of a distance between the fixed cylinder and the rotating cylinder to the outer radius of the rotating cylinder is greater than 0.05 and less than 0.4, wherein the reaction fluid has a kinematic viscosity of 0.4 to 400 cP and the reactor has a power consumption per unit mass of 0.05 W/kg to 100 W/kg, wherein the power consumption per unit mass is defined as a stirring rate of the rotating cylinder, and the vortex pairs have a critical Reynolds number of 300, wherein the composite transition metal hydroxide particles are prepared by introducing, into the rotating reaction space of the reactor, an aqueous solution of raw materials including an aqueous solution of at least two transition metal salts and a basic aqueous solution so as to maintain pH of the aqueous solution of raw materials at a constant level of 10 to 12 via the inlet of the reactor and performing co-precipitation thereof in a non-nitrogen atmosphere for 1 to 6 hours, and the composite transition metal hydroxide particles comprising at least two transition metals and having an average diameter of 1 μm to 5 μm, wherein the composite transition metal hydroxide particles exhibit monodisperse particle size distribution and have a coefficient of variation of 0.2 to 0.7, wherein the composite transition metal hydroxide particles contain an impurity derived from a transition metal salt for preparation of a composite transition metal hydroxide, wherein an amount of the impurity is 0.3 wt% to 0.4 wt% based on a total weight of the composite transition metal hydroxide particles.