We report a theoretical investigation on the magnetocaloric properties of the cubic CsCl-type TbZn compound. Two successive peaks in the magnetocaloric quantities are observed and attributed to different types of phase transitions. For the magnetic field applied in the <110> direction, the first peak is ascribed to a spontaneous first-order spin reorientation transition (SRT) at T1=63 K, and the second one to the ferroparamagnetic phase transition. The application of an external magnetic field of 2 T along this direction leads to a tablelike behavior in the magnetocaloric quantities (ΔST and ΔTS) as a consequence of two successive second-order SRTs at TSR1=71 K and at TSR2=160 K. Applying a magnetic field of 5 T suppress the flat behavior but a high refrigeration capacity of 352 J/kg is predicted in a wide temperature range from 62 to 258 K. When the magnetic field is applied along the <100> direction an inverse magnetocaloric effect is observed in the temperature range below T1. The system was studied throughout a Hamiltonian that takes into account the Zeeman, exchange, and crystal field interactions.