The nonlinear optical properties of semiconductor nanowires are of vital importance in the researches of nano-optics and fabrication of nano-scale optoelectronic components. GaAs is a direct bandgap semiconductor material of wide bandgap, high electron mobility, large χ(2), high laser damage threshold and stable chemical properties, all of which make it a potential nonlinear optical material. In this report, based on the finite element method (FEM), we investigated the optical response and local field enhancement of GaAs nanowires perpendicular to the GaAs substrate surface. Under the radiation of femto-second laser pulses at different wavelengths, efficient second harmonic generation (SHG) signal was acquired from the nanowires. Furthermore, noise-free broadband SHG signal was also detected to be excitated by super-continuous femto-second pulses (1000-1300 nm). The high-efficiency SHG process could be attribated mainly to the local field enhancement effect of the nanowires. Our investigation is the first, as far as we know, demonstrate the SHG properties of GaAs nanowires, and the results suggest that GaAs nanowires are promising in the potential applications in nano-scale optical devices, integrated nanophotonic circuits, from which related nano-optics researches can benefit.