We report the transit observations of the ultra-hot Jupiter WASP-121b using the Goodman High Throughput Spectrograph at the 4 m ground-based Southern Astrophysical Research Telescope, covering the wavelength range 502–900 nm. By dividing the target and reference star into 19 spectroscopic passbands and applying differential spectrophotometry, we derive spectroscopic transit light curves and fit them using a Gaussian process framework to determine transit depths for every passband. The obtained optical transmission spectrum shows a steep increased slope toward the blue wavelength, which seems to be too steep to be accounted for by Rayleigh scattering alone. We note that the transmission spectrum from this work and other works differ obviously from each other, which was pointed out previously by Wilson et al. as evidence for temporal atmospheric variation. We perform a free chemistry retrieval analysis on the optical transmission spectra from this work and the literature HST/WFC3 NIR spectrum. We determine TiO, VO and H2O with abundances of \(-5.95_{-0.42}^{+0.47}\) dex, \(-6.72_{-1.79}^{+0.51}\) dex and \(-4.13_{-0.46}^{+0.63}\) dex, respectively. We compare the abundances of all three of these molecules derived from this work and previous works, and find that they are not consistent with each other, indicating the chemical compositions of the terminator region may change over long timescales. Future multi-epoch and high-precision transit observations are required to further confirm this phenomenon. We note that when combining the transmission spectra in the optical and in NIR in retrieval analysis, the abundances of V and VO, the NIR-to-optical offset and the cloud deck pressure may be coupled with each other.