A spindle drive for a motorized adjustment of an adjustment element of a motor vehicle includes a tubular or half-shell-like spindle drive housing. An annular or disk-like connection portion is inserted and secured in one end region of the spindle drive housing. The annular or disk-like connection portion is connected via a damping element comprising a resilient damping material to a connection for discharging axial drive movements. The connection portion has a coaxial recess with an inner radially peripheral wall having a radially peripheral groove. The connection with the end region thereof facing the spindle drive housing protrudes axially into the recess of the connection portion and has a radially peripheral flange which protrudes radially into the groove. The damping element is arranged in a gap disposed between the side walls of the groove and the side walls of the flange.