A sufficient stability condition for time-domain magnetic field integral equations (TDMFIE) based on marching on-in time (MOT) algorithm is obtained through theoretical derivation using the norm. If the condition is satisfied, it can be ensured that the computational results will always be stable in late-time no matter what kind of incident wave is. Moreover, a factor expressing the recursive relationship of the currents is obtained, which can represent the constringency of the currents. Finally, the sufficient stability condition is validated by numerical results. Meanwhile, the numerical results also verify that the factor can be used to represent the stability of the currents.