We present an ultrahigh resolution optical fiber strain sensor with a broad frequency range from quasi-static to several hundred hertz. The sensor consists of a π-phase shifted fiber Bragg grating for strain sensing and a fiber Fabry-Perot interferometer as reference. The laser carrier and sideband are locked to the reference and sensing elements, respectively, via two individual feedback loops, in which the Pound-Drever-Hall technique is employed to generate the error signals. The sampling rate is up to 500 samples/s in the demonstrational experiments, only limited by the updating rate of the frequency counter. The strain resolution exhibits a 1/f characteristic in the bandwidth of 0.01-250 Hz, and is better than 0.01 nϵ at 10 Hz with a dynamic range up to 149 dB. Compared with the traditional static strain sensors, the proposed sensor shows a great improvement in both resolution and sensing bandwidth, and can be a powerful tool for geophysical applications.