An apparatus for mixing viscous material includes a chamber having a cylindrical sidewall and a bottom and receiving viscous material to be mixed; a cylindrical draft tube fixed at an inside center of the chamber to be spaced from the bottom and the sidewall and forming a space between the draft tube and the sidewall to allow passage of the viscous material, and including a heat medium passage therein; a carrying impeller installed in the draft tube and driven by a motor to transfer the viscous material above or below the draft tube and suck the viscous material in the space into the draft tube; and a sweeping impeller installed in the space and rotated in a circumferential direction by a motor to apply a pressure to the viscous material so that the viscous material in the space is not adhered to the draft tube and the sidewall.