The hash function Skein is one of the five finalists of the NIST SHA-3 competition. It is based on the block cipher Threefish which only uses three primitive operations: modular addition, rotation and bitwise XOR (ARX). This paper studies the boomerang attacks on Skein-512. Boomerang distinguishers on the compression function reduced to 32 and 36 rounds are proposed, with time complexities 2^104.5 and 2^454 hash computations respectively. Examples of the distinguishers on 28 and 31 rounds are also given. In addition, the boomerang distinguishers are applicable to the key-recovery attacks on reduced Threefish-512. The time complexities for key-recovery attacks reduced to 32-/33-/34-round are about 2^181, 2^305 and 2^424 encryptions. Because the previous boomerang distinguishers for Threefish-512 are in fact not compatible [14], our attacks are the first valid boomerang attacks for the reduced-round Skein-512.