The invention relates to an arrangement for damping oscillation of a loading member in a crane comprising a trolley (2), a hoisting mechanism located in the trolley, a hoisting rope (4) suspended from the hoisting mechanism, a loading member (5) fastened to the hoisting rope, the arrangement for damping oscillation of a loading member comprising a vertical guide projection (8) arranged in an upper part of the loading member, a guide tube (9) fastened to the trolley for receiving the guide projection, damping members arranged in the guide tube and com- prising elastic guide roll structures (10) engaging around the guide projection, each guide roll structure comprising a roll frame (11) and a guide roll (12) installed therein. Each roll frame is installed on an outer surface of the guide tube,a wall of the guide tube is at each guide roll provided with an opening (13) from which the guide roll penetrates into the guide tube, and elasticity is arranged between the roll frame and the guide tube.