In order to extract bearing information from the directional sensors of DIFAR(directional frequency analysis and recording) that is a kind of passive sonobuoy, the cardioid beamforming algorithm applicable to DIFAR system was studied in the frequency domain. the algorithm uses narrow-band signals propagated though the media from the acoustic sources such as ship machineries. The proposed algorithm is expected to give signal to noise ratio of 6dB when it uses the maximum response axis(MRA) among the Cardioid beams. The estimated bearings agree very well with those from GPS data. Assuming the bearings from GPS data to be real values, the estimation errors are analyzed statistically. The histogram of estimation errors in each frequency have Gaussian shape, the mean and standard deviation dropping in the ranges -1.1~$6.7^{circ}$ and 13.3~$43.6^{circ}$, respectively. Estimation errors are caused by SMR degradation due to propagation loss between the source and receiver, daily fluctuating geo-magnetic fields, and non-stationary background noises. If multiple DIFAR systems are employed, in addition to bearing, range information could be estimated and finally localization or tracking of a target is possible.