Method of building an offshore windmill on a windmill pedestal that is located offshore, characterized in that the method comprises: - providing a floating vessel comprising a 3D-heave-compensated crane on a deck thereof; - providing at least one offshore windmill assembly (110, 120, 130) and a lifting jack, wherein the offshore windmill assembly comprises a windmill generator, a plurality of windmill blades (130, 130-1..130-3) and at least two windmill column parts (110, 110-1..110-3) for forming a windmill column at a later stage, wherein the lifting jack is configured for receiving the windmill column (110-1..110-3) in a receiving region thereof; - moving said floating vessel, the lifting jack and the at least one offshore windmill assembly (110, 120, 130) in proximity of the windmill pedestal; - placing the lifting jack directly on the windmill pedestal using the 3D-heave-compensated crane and fixing the lifting jack to the windmill pedestal such that it can be later removed, and wherein the lifting jack is fixed to the windmill pedestal such that the windmill column (110-1..110-3) can be placed within the receiving region directly on the windmill pedestal; - installing the windmill generator using the 3D-heave-compensated crane; - partially erecting the windmill column (110-1..110-3) on the windmill pedestal using the 3D-heave-compensated crane and the lifting jack; - installing the windmill blades (130, 130-1..130-3) on the windmill generator using the 3D-heave-compensated crane at a stage where the windmill column (110-1..110-3) has been partially erected; - fully erecting the windmill column (110-1..110-3) on the windmill pedestal using at least the lifting jack; - removing the lifting jack from the windmill pedestal using the 3D-heave-compensated crane. - providing a floating vessel comprising a 3D-heave-compensated crane on a deck thereof; - providing at least one offshore windmill assembly (110, 120, 130) and a lifting jack, wherein the offshore windmill assembly comprises a windmill generator, a plurality of windmill blades (130, 130-1..130-3) and at least two windmill column parts (110, 110-1..110-3) for forming a windmill column at a later stage, wherein the lifting jack is configured for receiving the windmill column (110-1..110-3) in a receiving region thereof; - moving said floating vessel, the lifting jack and the at least one offshore windmill assembly (110, 120, 130) in proximity of the windmill pedestal; - placing the lifting jack directly on the windmill pedestal using the 3D-heave-compensated crane and fixing the lifting jack to the windmill pedestal such that it can be later removed, and wherein the lifting jack is fixed to the windmill pedestal such that the windmill column (110-1..110-3) can be placed within the receiving region directly on the windmill pedestal; - installing the windmill generator using the 3D-heave-compensated crane; - partially erecting the windmill column (110-1..110-3) on the windmill pedestal using the 3D-heave-compensated crane and the lifting jack; - installing the windmill blades (130, 130-1..130-3) on the windmill generator using the 3D-heave-compensated crane at a stage where the windmill column (110-1..110-3) has been partially erected; - fully erecting the windmill column (110-1..110-3) on the windmill pedestal using at least the lifting jack; - removing the lifting jack from the windmill pedestal using the 3D-heave-compensated crane.