We demonstrate an accelerometer based on a dual-frequency DBR fiber laser with a resolution of 6 μg/Hz1/2 at 1 kHz. The accelerometer is implemented by mounting a 250-milligram proof mass onto the laser cavity and converting the vibration into change in beat frequency between the two orthogonal polarization lasing modes. Experimental result shows that the sensitivity reaches 1.7 MHz/g at 1 kHz with a working bandwidth over 1 kHz. The high resolution is also a result of the noise level as low as 10 Hz/Hz1/2 due to the compensation between the two lasing modes. The present accelerometer with extremely high resolution and light weight is promising for geophysical applications.