The electronic states of OsSi are calculated by multi-state N-electron valence state second order perturbation theory (MS-NEVPT2) with all-electron basis sets. The relativistic effects are considered comprehensively that allows us to identify the X-3 Sigma(-)(0+) ground state. The theoretical equilibrium bond length 2.103 angstrom is close to the experimental measurement of 2.1207 angstrom while the vibrational frequency 466 cm(-1) is smaller than the experimental value of 516 cm(-1). Two excited states, namely (3)Pi(1)(I) and (3)Pi(1)(II), are located at 15568 and 18316 cm(-1) above the ground state, respectively. The (3)Pi(1)(I) <- X-3 Sigma(-)(0+) transition has been assigned to the experimental spectra at 15729 cm(-1) and (3)Pi(1)(II) <- X-3 Sigma(-)(0+)may produce the bands near 18469 cm(-1). Although the latter transition energy is in accord with the experimental spectra, theoretical calculations give too small oscillator strength. Moreover, plenty of excited states with considerable oscillator strengths are located that could serve as reference data in future experiments. The four low-lying states of OsC are also calculated for comparison.