A sewing machine-driving apparatus forms an accurate and stable seam at a first stitch in a conventional double chain stitch or covering chain stitch sewing machine. Its motor is controlled so as to drive the sewing machine in a direction reverse to that of the usual sewing operation for a limited time period between the completion of a thread cutting operation and a point of time when the sewing machine needles reach their needle-down position. Thus, the stitching needles reach their lowest points without scooping a looper thread at the first stitch; assuring the formation of a stable and accurate seam in the second stitch.