A composite structure based on linearly chirped fiber Bragg grating which can compensate for dispersion and polarization mode dispersion simultaneously has been proposed and characterized. On one hand, a chirped fiber Bragg grating can be regarded as a filter that is composed of several uniform sub-gratings. Therefore, optical signals with different wavelengths can be reflected at different points of the grating, which will result in different time delays, by which the dispersion compensation can be implemented easily. On the other hand, a chirped fiber Bragg grating has the pressure-induced birefringence effect. In the experiment, a piezoelectric transducer is used to apply the pressure on the linearly chirped fiber Bragg grating. Then the change of reflection spectra can be obtained when the pressure is applied at different points of the grating. From the reflection spectra response, the transverse pressure is found to lead to the split of the spectra of the grating. Through the observation of the group delay characteristics, we find that the differential group delay moves towards a bigger value with the increased voltage, and the maximal range of differential group delay (DGD) is 50 ps. By consequence, first-order polarization mode dispersion (PMD) can be compensated for with linearly chirped fiber Bragg grating. Thus, when the data rate of the fiber communication system is above 10 Gb/s and below 40 Gb/s, the simultaneous compensation of DGD and PMD is necessary and can be achieved by the composite structure.