A simple and robust technique is reported to offset lock a single semiconductor laser to the atom resonance line with a frequency difference easily adjustable from a few tens of megahertz up to tens of gigahertz. The proposed scheme makes use of the frequency modulation spectroscopy by modulating sidebands of a fiber electro-optic modulator output. The short-term performances of a frequency offset locked semiconductor laser are experimentally demonstrated with the Allan variance of around 3.9×10 11 at a 2 s integration time. This method may have many applications, such as in Raman optics for an atom interferometer.