Based on more than 10 years of large-scale spectral sky survey, LAMOST DR9 v1.0 low resolution catalog has released 76167 data of QSOs. We adopt 48704 QSOs with redshift Z from 0.0 to 6.0, the error of redshift from 0.0 to 0.06, and the galactic latitude |b| > 30 degrees to do a research work. There are 95.36% of QSOs with the error of redshift less than or equal to 0.025. Therefore, the Z values are very reliable with small errors. Some statistical figures about Z are drawn and preliminarily analyzed. The distribution of QSOs with Z in different directions shows that universe is spatially isotropic in large-scale structure. The QSOs with high Z values and low Z values correspond to the decelerating and accelerating expansion of the universe respectively, the epoch of the matter dominance and the dark energy dominance respectively. In the epoch of matter dominance, the number density of QSOs in the statistical figures is more than that in the epoch of dark energy dominance and the gravity can slow the expansion. The large-scale spectral sky survey is helpful for us to better understand the past, present and future of the universe.