The invention relates to an arrangement for damping oscillation of a loading member in a crane comprising a trolley (2), a hoisting mechanism, hoisting ropes (4), a loading member (5) fastened to the hoisting ropes, the arrange- ment comprising a vertical guide projection (10) arranged in an upper part of the loading member, and a guide part (11) arranged in the trolley and receiving the guide projection, damping members (14, 15) connected to the guide part being arranged in a separate support frame (12) which,in a hoisting direction of the loading member,is guidable into its place in a dock (13) arranged un- derneath the trolley and which is lowerable off the dock, onto the loading member, the guide part being a floating guide tube structure (11),and the damping members comprising a plurality of side damping modules (14) con- nected between a side wall of the guide tube structure and the support frame, around the guide tube structure,for substantially damping horizontal move- ment of the guide tube structure, and a support joint (15) which is arranged in an upper part of the support frame and from which the guide tube structure is suspended.