A wrapping machine (1) comprises frame means (2, 8) for supporting a wrapping unit (3) arranged to wrap a load (100) with a film (50) of plastic material, and a covering apparatus (4) arranged to supply a covering sheet (60) and position it above the load (100); the covering apparatus (4) comprises a supplying unit (7) supporting a reel (61) of covering sheet (60) and gripping means (5) movable along an unwinding direction (F) and arranged to grip and unwind from the reel (61) the covering sheet (60) above the load (100); the supplying unit (7) includes roller means (21) for rotatably supporting the reel (61) of covering sheet (60) so that the reel (61) can rotate about a rotation longitudinal axis (Y); a drawing element (22) movable substantially orthogonally to the rotation longitudinal axis (Y), between a gripping position (W1), wherein the drawing element (22) is arranged to receive and retain an initial flap (62) of the covering sheet (60) unwound from the reel (61), and a releasing position (W2), wherein said drawing element (22) after partially unwinding the covering sheet (60) positions the initial flap (62) at a front portion (17) of the supplying unit (7) from which the covering sheet (60) comes out; and locking means (23) for retaining the initial flap (62) moved by the drawing element (22) at a front portion (17) of the supplying unit (7), the initial flap (62) being so arranged to be gripped by the gripping means (5).