A scroll sawing machine includes a first transmitting shaft driven by an output shaft of a motor, a second transmitting shaft rotatable to move a blade-driving member in an upright direction so as to enable a saw blade to perform reciprocating movement, and a speed ratio varying device disposed to couple the transmitting shafts. The device includes two pitch-variable first and second pulleys mounted on the transmitting shafts, a belt trained on the pulleys, and a control unit operable to move a movable disc of the first pulley toward or away from a fixed disc of the first pulley so as to vary the radial distances between the belt and each of the transmitting shafts, thereby varying the speed ratio of the second transmitting shaft to the first transmitting shaft.