In twin-roll casting, as heat is transferred from melt to rolls, the melt is cooled, solidified and finally rolled to a specific thickness. Therefore, an efficient cooling system for the roll is very important for a stable operation of the process. In the present study, a composite roll with internal cooling channels was designed for twin-roll casting of magnesium alloy AZ31 by considering steady-state heat transfer between objects. The roll consisting of a steel core and a copper alloy sleeve was proposed to be assembled by thermal-shrinkage fitting. The fitting strength was examined by a series of stress analyses at stages of assembly as well as operation. The number of cooling channels and their cross sections were modified accordingly.