Method for mounting a wind turbine on a tower; the method comprises: a) defining support points in a region close to an upper end of the tower, and in two opposite sides thereof, and mounting a support frame on said support points; b) mounting on the support frame winches arranged on two opposite sides of the tower; c) providing a support structure, comprising two longitudinal, parallel and braced beams, on which a first gantry and a second gantry capable of longitudinal displacement are mounted; and placing the support structure around the base of the tower, with the longitudinal beams arranged on two opposite sides of the tower, the gantries (402, 403) projecting from other two opposite sides of the tower; d) arranging the nacelle on the end of the support structure corresponding to the first gantry and arranging the rotor with the blades horizontally on the other end of the support structure corresponding to the second gantry; e) lifting in a stabilized manner the support structure carrying the nacelle and rotor with the blades, by means of the winches, to the upper end of the tower; and the horizontal stabilization of said support structure by cables (404, 405) attached to ground anchor jacks and to the ends of the support structure provided with the first gantry and the second gantry; f) rotating the rotor with the blades from a horizontal position to a vertical position while the support structure is being lifted; g) positioning and anchoring the support structure on the support frame by means of the longitudinal beams; h) displacing the first gantry carrying the nacelle on the longitudinal guides of the support structure to a mounting position of the nacelle on the upper end of the tower; mounting the nacelle on the tower, and displacing the first gantry on the longitudinal beams returning back to its original position; stabilizing the support structure during these movements by actuation of the jacks on the cables attached to the ends of the support structure corresponding to the first gantry; such that the weight of the loads is transmitted almost vertically to the tower; i) displacing the second gantry carrying the rotor with the blades on the longitudinal guides to a mounting position in the nacelle; the second gantry returning back to the initial position once the rotor with the blades has been mounted in the nacelle and stabilizing the support structure during these movements by actuation of the jacks on the cables attached to the end of the structure corresponding to the second gantry; j) lowering the structure and disassembling the winches and the frame. a) defining support points in a region close to an upper end of the tower, and in two opposite sides thereof, and mounting a support frame on said support points; b) mounting on the support frame winches arranged on two opposite sides of the tower; c) providing a support structure, comprising two longitudinal, parallel and braced beams, on which a first gantry and a second gantry capable of longitudinal displacement are mounted; and placing the support structure around the base of the tower, with the longitudinal beams arranged on two opposite sides of the tower, the gantries (402, 403) projecting from other two opposite sides of the tower; d) arranging the nacelle on the end of the support structure corresponding to the first gantry and arranging the rotor with the blades horizontally on the other end of the support structure corresponding to the second gantry; e) lifting in a stabilized manner the support structure carrying the nacelle and rotor with the blades, by means of the winches, to the upper end of the tower; and the horizontal stabilization of said support structure by cables (404, 405) attached to ground anchor jacks and to the ends of the support structure provided with the first gantry and the second gantry; f) rotating the rotor with the blades from a horizontal position to a vertical position while the support structure is being lifted; g) positioning and anchoring the support structure on the support frame by means of the longitudinal beams; h) displacing the first gantry carrying the nacelle on the longitudinal guides of the support structure to a mounting position of the nacelle on the upper end of the tower; mounting the nacelle on the tower, and displacing the first gantry on the longitudinal beams returning back to its original position; stabilizing the support structure during these movements by actuation of the jacks on the cables attached to the ends of the support structure corresponding to the first gantry; such that the weight of the loads is transmitted almost vertically to the tower; i) displacing the second gantry carrying the rotor with the blades on the longitudinal guides to a mounting position in the nacelle; the second gantry returning back to the initial position once the rotor with the blades has been mounted in the nacelle and stabilizing the support structure during these movements by actuation of the jacks on the cables attached to the end of the structure corresponding to the second gantry; j) lowering the structure and disassembling the winches and the frame.