The structures, stability and spectroscopic property of Chromium doped small silicon clusters CrSin (n=3～9) and their anions are systematically investigated using CCSD(T)/aug-cc-pVTZ-DK//MP2/6-31G(2df, p) and the B3LYP/ aug-cc-pVTZ basis set. The results show that the ground-state structures of neutral CrSin (n=3～9) and their anion are all exohedral structures. According to the calculated dissociation energies, it shows that when n<5, the neutral CrSin are less stable than their anion. And when n≥5, the CrSi5 and CrSi8 of neutral CrSin are more stable than their neighboring clusters; the CrSi4 and CrSi7 of anionic CrSin are less stable than their neighboring clusters. The VDEs of CrSin are predicted to be 2.26 eV for CrSi3, 3.21 eV for CrSi4, 2.72 eV for CrSi5, 3.54 eV for CrSi6, 2.45 eV for CrSi7, 2.71 eV for CrSi8 and 2.95 eV for CrSi9. They are in excellent agreement with experimental data except for CrSi4, the average absolute deviations from experimental data are only 0.073 eV. The AEAs of CrSin are evaluated to be 2.07 eV for CrSi3, 1.95 eV for CrSi4, 2.4 eV for CrSi5, 2.32 eV for CrSi6, 2.38 eV for CrSi7, 2.67 eV for CrSi8, and 2.63 eV for CrSi9. Except for CrSi6, they are in excellent agreement with experimental data. The average absolute deviations from experimental data are only 0.09 eV. Besides, the photoelectron spectra (PES) of ground-state structures of anionic CrSin (n=3～9) are simulated at the PBE1PBE/6-31G(2df, p) level, and compared to the corresponding experiment data, it is concluded that the ground-state structures obtained in this paper are reliable.