Usually an induction machine with closed slots on the rotor has lower harmonics in stator line currents than that with open slots. However, some induction machines with closed-rotor slots may suffer from local saturation in the rotor slot bridges, and thus, exhibit significant low-order time harmonics in the stator currents. Such phenomenon is revealed with theoretical analysis, and validated with both finite element analysis and experiments. This study is of reference value for the induction machine design so as to avoid the low-order current harmonics.