This study proposes a novel five-level three-phase hybrid-clamped converter composed of only six switches and one flying capacitor (FC) per phase. The capacitor-voltage-drift phenomenon of the converter under the classical sinusoidal pulse width modulation (SPWM) strategy is comprehensively analyzed. The average current, which flows into the FC, is a function of power factor and modulation index and does not remain at zero. Thus, a specific modulation strategy based on space vector modulation (SVM) is developed to balance the voltage of DC-link and FCs by injecting a common-mode voltage. This strategy applies the five-segment method to synthesize the voltage vector, such that switching losses are reduced while optional vector sequences are increased. The best vector sequence is then selected on the basis of the minimized cost function to suppress the divergence of the capacitor voltage. This study further proposes a startup method that charges the DC-link and FCs without any additional circuits. Simulation and experimental results verify the validity of the proposed converter, modulation strategy, and precharge method.