The K-edge of X-ray absorption near edge structure (XANES) spectra can provide in-situ geometric and electronic information about transition metal catalyst. Due to the complicated characters of the K-edge absorptions, theoretical studies are indispensable to extract such quantitative features. The present work focused on K-edge absorptions of a series of vanadium complex catalysts. The linear-response time-dependent density functional theory (LR-TDDFT) and real-time time-dependent density functional theory (RT-TDDFT) method have been used to calculate the K-edge XANES spectra. The pre-edge region can be well reproduced by LR-TDDFT. The peaks appearing in the pre-edge region were assigned to dipole-allowed transitions of $1s$ electrons to the $3d4p$ hybridized orbitals. However, the shoulder peak region located on the K-edge cannot be fully explained by LR-TDDFT calculation due to the complicated multiple excitations and large density rearrangement where the linear response approximation is no longer valid. The greatest strength of RT-TDDFT is that it can produce the entire broad-band spectrum within a single calculation, which happens to serve as a supplement to LR-TDDFT. Recently, Herbert et al. have developed and implement an efficient RT-TDDFT algorithm for computation of X-ray absorption spectra of small molecules. [J. Chem. Phys. 2018, 148, 044117] Herein, we have applied this RT-TDDFT algorithm to probe the absorption features on the raising K-edge. Based on our RT-TDDFT calculations, we have successfully assigned shoulder peaks on the K-edge and characterized the electronic properties of vanadium complexes.