An acceleration/deceleration control apparatus for a numerical control apparatus which controls a tool in a vicinity of a stroke end by making maximum use of a stroke. The tool moves along a locus in an in-stroke region surrounded by a stroke end and carries out machining of a workpiece such as cutting and the like. The tool, which is moved by the numerical control apparatus according to a machining program, starts from a start point and moves up to an end point in accordance with preread machining blocks. The tool moves in response to usual feed speed control except that tool feed speed is decelerated in sections of the machining blocks when the tool approaches the stroke end. The tool feed speed is controlled to a minute speed just before the tool reaches the boundary of the stroke end and maintains the minute speed while moving along the stroke end. The tool is then accelerated after moving from the stroke end and returns to usual feed speed control.