The elastic, electronic, and optical properties of zinc-blende structure GaN under high pressure are investigated by using a first-principles ultra-soft pseudo-potential approach of the plane wave based on the density functional theory. The calculated results show the dependences of the elastic constant, the bulk modulus, the young modulus, and the energy gap on the applied pressure, and the results are in good agreement with the experimental and theoretical values. Furthermore, the dielectric function, optical reflectivity, refractive index, absorption coefficient and energy-loss function of GaN are analyzed in terms of the accurately calculated band structure and density of state. The conclusions drawn from the calculations offer theoretical basis for the design and application of GaN.