Using first-principles total energy calculations, we have studied the structural, mechanical and electronic properties of GaAs_1-xN_x ternary semiconductor alloys with the zinc-blende crystal structure over the whole nitrogen concentration range (with x from 0 to 1) within density functional theory (DFT) framework. To obtain the ideal band gap, we employ the semi-empirical approach called local density approximation plus the multiorbital mean-field Hubbard model (LDA+U). The calculated results illustrate the varying lattice constants and band gap in GaAs_1-xN_x alloys as functions of the nitrogen concentration x. According to the pressure dependence of the lattice constants and volume, the higher N concentration alloy exhibits the better anti-compressibility. In addition, an increasing band gap is predicted under 20 GPa pressure for GaAs_1-xN_x alloys.