By efficient frequency doubling of 1560 nm distributed feed back laser with a MgO:PPLN waveguide, the laser frequency is locked to the D2 hyperfine transition of 87Rb atoms via radio-frequency frequency modulation spectroscopy (RF-FMS) and modulation transfer spectroscopy (MTS). The theories, spectra and frequency locking results of the two schemes are compared. The root mean squares of frequency fluctuation with feedback using the two schemes are ±135 kHz and ±85 kHz, respectively, while it is 8~10 MHz for free running. This is owing to the better signal-to-noise ratio and completely no background for MTS. Utilizing MTS, a compact, robust 1.5 μm laser system for fiber-optic communication application is built.