A machine, particularly for producing cellulose fiber from waste paper with characteristics and yield comparable to virgin fiber, includes at least one conveyor body which is adapted to receive the waste material from which to obtain cellulose fiber; and at least one drum which contains inside it grinders adapted to grind the waste material for the production of the cellulose fiber, and which communicates with the conveyor body. The grinders include a grinding hammer which is arranged on the bottom of the drum and can rotate by way of a motor about a rotation axis.