In order to choose appropriate frequency stabilization method in the atom gravimeter system under construction, Doppler-free dichroic atomic vapor laser lock(Doppler-free DAVLL) and saturated absorption spectroscopy(SAS) method were implemented on Rubidium atomic vapor. Basic principle and experimental details of both frequency stabilization methods were introduced. With restructuring of optical path and applying of self-made low noise photoelectric detector as well as digital lock module, excellent error signal was obtained. For each method, two sets of locking system were built and kept locked during 3 000 s′ data acquisition. A frequency fluctuation of 629 kHz when the laser is free running and of 16.2 kHz & 31.4 kHz after locked by SAS and Doppler-free DAVLL were calculated respectively, corresponding to a frequency stability of 1.64×10-9 in the condition of free running and 4.21×10-11 & 8.18×10-11 after locked for averaging time of 10 s. The strength and weakness of both methods were elaborated with the demand of system miniaturization. After compared with SAS, Doppler-free DAVLL isconsidered to be a promising choice for miniaturization and modularization in atom interferometry gravimeter.