Combining light modulation and frequency conversion techniques, a compact and simple frequency-stabilized optical frequency comb spanning over 45 nm in the 1.56-μm wavelength region is demonstrated. It benefits from the high-frequency stability achievable from rubidium atomic transitions at 780 nm probed in a saturation absorption scheme, which is transferred to the 1.56-μm spectral region via a second-harmonic generation process. The optical frequency comb is generated by an electro-optic modulator enclosed in a Fabry-Perot cavity that is injected by the fundamental frequency stabilized laser. Frequency stability better than 2 kHz has been demonstrated on time scales between 1000 s and 2 days both at 1560 nm, twice the rubidium wavelength, and for a comb line at 1557 nm.