A composite filter apparatus includes a container with a receiving space, and top and bottom openings communicated with the receiving space. A filter member includes a filter core in the receiving space, a blocking member on a top end of the filter core, and a retainer plate on a bottom end of the filter core. The receiving space is divided by the blocking member into an upper receiving space that communicates the top opening of the container, and a lower receiving space that surrounds the filter core and that communicates the bottom opening. Activated carbon particles are filled in the upper and lower receiving spaces.