This paper proposes a new method for constant control of the output AC voltage of a voltage-fed three phase Z-source inverter (ZSI), in case of Z-network DC voltage variation or heavy change of load. The modulation index for the reference output AC voltage of ZSI can be calculated by the basic definition of ZSI, the input DC voltage and capacitor voltage of Z-network. And, the output AC voltage of ZSI is controlled by the modified space vector modulation (SVM) with the calculated modulation index. By the proposed method, the modulation index of output AC voltage is closely following in the reference modulation index. The validity of the proposed method is verified using PSIM simulation. In case which the input DC voltage of ZSI is heavily changed from 100[V] to 70[V] (or to 150[V]) and in case which load is changed from 30[Ω] to 10[Ω], we confirmed that the output AC voltage of ZSI is constantly controlled by the proposed method because the modulation index of ZSI is also simultaneously changed. Finally, FFT and %THD of the output voltage and current of ZSI by the proposed method are analyzed.