This paper proposes a novel design for variable-flux machines with Alnico magnets. The proposed design uses tangentially magnetized magnets to achieve high air-gap flux density and to avoid demagnetization by the armature field. Barriers are also inserted in the rotor to limit the armature flux and to allow the machine to utilize both reluctance and magnet torque components. An analytical procedure is first applied to obtain the initial machine design parameters. Then, several modifications are applied to the stator and rotor designs through finite-element analysis (FEA) simulations to improve machine efficiency and torque density. A prototype of the proposed design is built, and the experimental results are in good correlation with the FEA simulations, confirming the validity of the proposed machine design concept.