The three-phase dual-active bridge converter (3pDAB) is becoming a promising topology due to the advantages of higher power density and efficiency. Under phase-shift (PS) modulation, the phase-shift angle will have a significant step change when the transmission power is quickly adjusted, which will cause serious transient oscillation of the inductance current and pose a risk to the safety of the converter. Focusing on the widely utilized single-phase-shift (SPS) modulation, this paper examines the transient process of 3pDAB resulting from variations in the phase-shift angle. Then, by temporarily adjusting the external phase-shift angle, a fast transient current control strategy (FTCC) is proposed to mitigate oscillations, effectively managing the transient process within one-third of a switching cycle and facilitating smooth transmission power adjustments. Furthermore, the impact and oscillation of inductance current during transient process are significantly reduced. Finally, the performance of the control strategy was verified.