Using the first-principles method based on density functional theory, at the generalized gradient approximation (GGA), the state density, the change of binding energy and the energy gap of the silicon nanocrystals (Si75H76) with the circumstances of boron (B)-doped , phosphorus (P)-doped and the surface modification with ethyl (CH2CH3), isopropyl (-CH(CH3)2) have been calculated. The results showed that the B or P-doped have little impact on the energy gap value (3.12 eV) of silicon nanocrystals (SiNcs), except that some energy levels will be introduced in the forbidden band. The energy level caused by three-coordinated B-doped SiNcs is E(c)-0.8 eV, while it is E(v) + 0.2 eV for the three-coordinated P-doped. However, the energy level position is E(v) +0.4 eV for the four-coordinated B-doped SiNcs, and E(c) -1.1 eV for the four-coordinated P-doped. Total energy of the system with the four-coordinated doped is lower than that with the three-coordinated doped in the other same conditions. The total energy of SiNcs system lessen when the surface is modified with appropriate ethyl or isopropyl. The total energy decreases with the surface coverage of organo-functional group increasing. But, the calculation can't converge because of too high resistance when the SiNcs surface are grafted with too many organic groups.