To explore the structural and electronic properties of SnSe under pressure, we applied hydrostatic pressure from 0 to 8 GPa to a fully relaxed SnSe cell sample based on plane-wave pseudopotential density functional theory. The calculated results indicate that the structure of SnSe changes gradually from an irregular zigzag structure with low symmetry to a B1-like structure with regular arrangement and high symmetry under pressure. The lattice parameters and cell volume of SnSe decrease monotonically as the applied pressure increases. The energy band gap of SnSe becomes narrow under pressure and is finally closed at 6.1 GPa. Moreover, we found that SnSe exhibits non-magnetic and semi-metallic features based on analyzing its electronic state density and spin state density. This can be attributed to the decrease in the lattices constants and the enhancement of the Sn-Se bond interaction under pressure, which causes the density of electronic states to increase near the Fermi surface. Finally, the charge distribution between Se-Sn-Se along the c-axis changes gradually from asymmetric to symmetric as the pressure is increased to 6.1 GPa and beyond. This implies that enhancement of the structure symmetry of SnSe can lead to a symmetrical distribution of charges, which further affects the bonding characteristics of the Sn-Se bond.