Phase noise of Raman lasers is a major source of noise for a Raman-type cold atom interferometer, which is traditionally measured using the signal source analyzer. We report here an atom-based method to measure the phase noise performance between two Raman lasers. By analyzing and calibrating the system noise sources, we can characterize the contribution of phase noise from the total deviation of the relative atom population at the middle of the interference fringe. Knowing the transfer function specified by the operation sequence of the interferometer, we can obtain the transfer function and power spectrum density of the phase noise term. By varying the time sequences of the interferometer, we can measure the white phase noise floor and the phase noise performance over a large range of Fourier frequencies from 1 to 100 000 Hz with a minor difference of 1 dB compared with results from the traditional method using a signal analyzer, which proves the validity of the atom-based method. Compared with the traditional measurement method, the atom-based method can have higher accuracy and have the ability of self-calibrating.