The conventional ZSVM3 (quasi-Z-source space vector modulation) has been used for quasi-Z-source rectifier because it achieves zero voltage switching(ZVS) and zero current switching(ZCS) operation with wide range of output power and without any auxiliary circuits. However, this method can not realize ZVS or ZCS at fully switching period, especially at the sector boundary, leading to low efficiency. To address this problem, in this paper, a modified modulation based on ZSVM3 is proposed. The sequence of active vectors and zero vectors has been modified. Therefore, the ZVS and ZCS operation occurs at any time in one switching cycle, and the conduction losses decrease. Besides, the distribution of Mode 3 duration time is optimized, which increases the range of soft switching conditions. The operating principle of the proposed modified SVM is explained in detail. Then the parameters design is developed. An experimental prototype is constructed to verify the effectiveness of the proposed modulation. Experimental results show that the grid-side THD and conduction losses reduce, all switches and free-wheeling diodes realize ZVS and ZCS operation at full range without any auxiliary circuit, and the highest efficiency is up to 96.87%.