Method for erecting a tower of a wind turbine comprising the steps of: - arranging a first tower segment on a foundation or a tower segment, wherein the first tower segment has a first and second centring mandrel at the upper side thereof, wherein the first centring mandrel has a shorter guiding portion than the second centring mandrel, wherein the first and second centring mandrel are constructed to be secured to a first tower segment of a concrete tower of a wind turbine and to guide a second tower segment of the concrete tower when the second tower segment is lowered onto the first tower segment and has a securing portion for securing to the first tower segment, a guiding portion for guiding the second tower segment, wherein the securing portion has an outer thread, in particular a metal thread, for screwing into the first tower segment, wherein the guiding portion is constructed in a conical manner and tapers in a direction facing away from the securing portion, wherein the securing portion and the guiding portion are constructed concentrically around a common axis, - the second tower segment is partially lowered onto the first tower segment in such a manner that a first centring mandrel partially engages in a corresponding first centring recess at the lower side of the second tower segment, - the second tower segment is pivoted about an axis of the first centring mandrel and the corresponding first centring receiving member until a second centring receiving member is arranged at the lower side of the second tower segment approximately above the second centring mandrel, - the second tower segment is completely lowered, wherein the first and second centring mandrel engage in the first and second centring recess of the second tower segment, respectively, in such a manner that the second tower segment is guided in the desired orientated position thereof on the first tower segment. - arranging a first tower segment on a foundation or a tower segment, wherein the first tower segment has a first and second centring mandrel at the upper side thereof, wherein the first centring mandrel has a shorter guiding portion than the second centring mandrel, wherein the first and second centring mandrel are constructed to be secured to a first tower segment of a concrete tower of a wind turbine and to guide a second tower segment of the concrete tower when the second tower segment is lowered onto the first tower segment and has a securing portion for securing to the first tower segment, a guiding portion for guiding the second tower segment, wherein the securing portion has an outer thread, in particular a metal thread, for screwing into the first tower segment, wherein the guiding portion is constructed in a conical manner and tapers in a direction facing away from the securing portion, wherein the securing portion and the guiding portion are constructed concentrically around a common axis, - the second tower segment is partially lowered onto the first tower segment in such a manner that a first centring mandrel partially engages in a corresponding first centring recess at the lower side of the second tower segment, - the second tower segment is pivoted about an axis of the first centring mandrel and the corresponding first centring receiving member until a second centring receiving member is arranged at the lower side of the second tower segment approximately above the second centring mandrel, - the second tower segment is completely lowered, wherein the first and second centring mandrel engage in the first and second centring recess of the second tower segment, respectively, in such a manner that the second tower segment is guided in the desired orientated position thereof on the first tower segment.