A filtering apparatus is provided for filtering raw water containing various impurities and mixtures into purified water, and more particularly, a multistage filtering apparatus is provided in which a rotor for generating vortex are installed in each of multiple layers of filtration membrane stacked within a closed barrel and the rotors are formed in multistage by having different diameter of each rotor so that the power for generating vortex can be remarkably minimized by generating the vertical vortex from top and bottom of the rotary rotor and the horizontal vortex from the outer side of circumference plate of the rotary rotor to be crossed over between membranes to prevent from blocking the pores or remove the deposited pollutants, and the closed-type barrel having multistage of membranes, rotary shaft, and rotary rotors for vortex generation within are constructed as a single module of filter pack, and the filter pack is connected and extended in accordance with required purified capacity so that large scale installation of filtering apparatus is possible.