Abstract: Self-climbing, telescopic crane and a method for mounting pre-fabricated concrete towers of the type formed by a plurality of modules joined laterally to form diverse frustroconical segments that are subsequently stacked to form the tower, that comprises an external vertical column and another internal one that can move vertically via actuators. The top part of the internal vertical column terminates in a horizontally rotatable capstan, associated with a horizontal arm terminating at the opposite end in a pulley through which the hoist cable moves. The invention presented affords the main advantage of allowing mounting from inside the tower, dispensing with the need of expensive long-reach cranes to be operating over long periods, with a notable reduction in the economic cost and the mounting time of the tower, as well as allowing mounting to be carried out in unfavourable wind conditions.