A trajectory display device comprises a position information acquisition part acquiring position information of a drive axis of a machine tool, a tool coordinate calculation part calculating the coordinate value of a tool tip point based on the position information, and a tool vector calculation part setting a tool vector along the tool axis with the tool tip point as the starting point. The trajectory display device comprises an intersection calculation part calculating the coordinate values of the intersection points of the tool vector with preset flat planes and a display part displaying the tool axis trajectories represented by a line connecting the intersection points.