First principles full-potential linearized augmented plane wave method with local density approximation (LDA) was applied to calculate the ground state properties of ReSi1.75 crystal. Optimized results show that the equilibrium lattice constant of ReSi1.75 is smaller than experimental data by about 0.6%. On the basis of LDA results, LDA+U method was used to calculate the electronic structure. When Ueff=U-J=4.4eV, ReSi1.75 has a narrow gap semiconductor band structure with an indirect gap of 0.12 eV and a direct gap of 0.36eV. Effective mass calculation shows the highly anisotropic character of ReSi1.75 crystals. The density of sates changes sharply near Fermi level，thus the thermoelectric properties can be improved by doping.