The newly developed cone drum twister is one of the outer surface contacting friction-twisting devices in false-twist texturing. An investigation of the drag angle for the newly developed cone drum twister texturing mechanism is reported. An analysis is given from which equations can be derived that relate to the conical angle of cone drum, wrapping angle, drag angle, and yam helix angle. Theoretical values of drag angle are calculated and discussed. It is shown that, as the helix angle and the projected wrapping angle increases, the drag angle also increases slowly until the helix angle of $40^{circ}$ but after the helix angle of $40^{circ}$ the drag angle increases rapidly. Furthermore the higher the projected wrapping angle and conical angle, the higher the drag angle of friction surface.