This paper proposes a quasi Z-source DVR(Dynamic Voltage Restorer) system with a series connection of the output terminals, to compensate the voltage variations in the 6.6[kV]/60[Hz] power distribution system. The conventional DVR using one quasi Z-source AC-AC converter has the advantage which it can compensate the voltage variations without the need for the additional energy storage device such as a battery, but it is impossible to compensate for the 50[%] under voltage sags. To solve this problem, a DVR system using two quasi Z-source AC-AC converters with the series connection of the output terminals is proposed. By controlling the duty ratio D in the buck-boost mode, the proposed system can control the compensation voltage. For case verification of the proposed system, PSIM simulation is achieved. As a result, in case that the voltage sags-swells occur 10[%], 20[%], 60[%] in power distribution system, and, in case that the 50[%] under voltage sags-swells continuously occur, all case could compensate by the proposed system. Especially, the compensated voltage THD was examined under the condition of the 10[%]~50[%] voltage sags and the 20[${Omega}$]~100[${Omega}$] load changes. The compensated voltage THD was worse for the higher load resistances and more severe voltage sags. Finally, In case of the voltage swells compensation, the compensation factor has approached nearly 1 regardless of the load resistance changes, while the compensation factor of voltage sags was related to the load variations.