Raman lasers generated by optical injection locking can be used in atom interferometers. However, phase noise significantly affects the phase of atom interference fringe; thus, we experimentally study the phase noise of the Raman laser under varying conditions. Two phase-locked Raman lasers exhibiting a frequency difference of 6.834 GHz are obtained by modulation of optical fiber electro-optic modulation (EOM) and injection locking. In the experimental system, the master laser is modulated using a 6.834-GHz fiber EOM, and its output is emitted as seed light. By adjusting the slave laser, the first amplification output beam of -1 level frequency-shifted laser can be obtained. The result demonstrates that the Raman laser beat linewidth is not wider than 3 Hz, the frequency is adjustable to 300 MHz, and the phase noise is less than -60 dBc/Hz from 10 Hz to 100 kHz when the master laser is frequency-locked.