A rowing machine is constructed to include a sloping angle-adjustable base frame, a foot rack selectively and pivotally mounted on the base frame at the front side, a rocker arm coupled with a detachable handlebar for rowing exercise to stretch elastic cord members, a slide slidably mounted on two parallel rails of the base frame to support a seat and a collapsible back, and two elastic pull cords detachably fastened to the base frame for pulling by the user sitting on the seat.