In a double-function sewing machine including a lock stitching mechanism and an overlock stitching mechanism a common driving source and a common flywheel for both stitching mechanisms are used. A switching device for switching the sewing machine from operation with the overlock stitching mechanism to the operation with lock stitching mechanism and vice versa is provided in the sewing machine. This device includes a belt wheel bush rotatable with respect to the machine frame and driven by the driving source and secured to the shaft of the flywheel, a belt wheel for overlock stitching rotatably supported with respect to the machine frame and connected to the overlock stitch forming mechanism, a ratchet guide member mounted on the main shaft of the lock stitch-forming mechanism and pivoted with respect to the machine frame, two sliding plates one of which is the mounted on ratchet guide member and another one of which is mounted on the belt wheel, and a switching lever. The switching lever is operated to alternatively hold one of the sliding plates on the belt wheel bush for selecting for operation the lock stitch-forming mechanism or the overlock stitch-forming mechanism.