The electron states as well as the nonlinear optical rectification and second and third harmonic generations are investigated in a GaAs-based V-groove quantum wire. The single band effective mass Schrödinger equation is solved using the finite element method. The nonlinear optical coefficients were calculated from expressions derived within the compact density matrix method. It is found that this kind of nanostructures can exhibit noticeable nonlinear responses in the domain of the terahertz when the V-groove is in the open-wide geometrical configuration.