A multi-strand steel cable includes steel strands jacketed with plastic fibers, where the plastic fiber jacketing is melted onto the steel strands by a thermal treatment. The steel cable has a core formed by an unjacketed steel strand, and the core is surrounded by jacketed steel strands. The heat supplied during the thermal treatment is introduced in such a way that certain areas of the steel strands which have been jacketed with the melted plastic fibers, namely, the areas adjacent to the core, are melted onto the outside circumference of the core.