The four-level Hybrid Clamped Converter (4L-HCC) is emerging as a promising DC/AC converter topology for high-efficiency medium-voltage drives. However, without proper control, the voltage fluctuation of the DC-link capacitors will be excessive, resulting in distorted AC current and stability issue in low frequency operation. In reality, the distorted current makes it impractical for motor drive during the rotor speed ramp up. This paper presents a control method of the HCC to reduce the DC link capacitor voltage fluctuations at very low frequency. Simulation results show that the proposed method can significantly reduce the capacitor fluctuation from 43% to 4.3% at 5 Hz and allow the HCC to operate at high steady-state frequency (60Hz). Meanwhile, a comparison study is conducted between the 4L-HCC and an equivalent 4-level Modular Multilevel Converter (4L-MMC). Compared to the equivalent MMC converter at very low frequency, the properly controlled HCC has more margin in DC bus voltage to generate high AC output voltage with a lower AC output current in THD and lower switching losses in power switches.