A trajectory display device capable of correctly quantifying an error of a three-dimensional trajectory of a machine tool, and displaying or outputting the error. The trajectory display device has a command line segment defining part adapted to define a command line segment which connects two temporally adjacent points, in relation to each commanded position; an error calculating part adapted to define a normal line extending from the actual position to each command line segment and calculate an error of the actual position relative to a commanded trajectory, the error being determined as a shorter one between a length of a shortest normal line among the defined normal lines and a length of a line segment extending from the actual position to a commanded position which is the nearest from the actual position.