The invention relates to a jet engine nacelle reverse thrust device (10) including a means for diverting at least one portion of a jet engine air flow and moreover includes at least one cowl (20) that is translatable in a direction substantially parallel to a longitudinal axis of the nacelle, the device having at least one flap (30) that is pivotably mounted, by one end, onto the translatable cowl, said translatable cowl (20) being capable of passing alternately from a closed position, wherein said cowl, with the flap (30) in a retracted position, ensures the aerodynamic continuity of the nacelle and covers the diverting means, to an open position, wherein said cowl opens a passage in the nacelle and uncovers the diverting means, the flap (30) being in a pivoted position wherein it is capable of sealing off a portion of an annular channel of the nacelle. The device also includes a system (40) for driving the flap (30), said system including at least one assembly forming a lever (50) that is pivotably mounted onto the cowl (20) and is hinged to each of the ends thereof by means of drive rods (61, 62), respectively located on the flap (30) and on a stationary structure (1) of the device.