The properties of the chirped fiber Bragg grating (CFBG) as a chromatic dispersion compensator in differential phase-shift-keyed (DPSK) transmission are analyzed. Comparisons of a performance of a CFBG in between DPSK and On-Off Key (OOK) are shown by simulations using the commercial numerical modeling software, $OptSim^{TM}$. In the simulation, we compared the performance of the CFBG when they were used in the RZ-OOK 40 Gbps and the RZ-DPSK 40 Gbps transmission. The simulation results show the performance of an overall transmission with a CFBG in DPSK is inferior to the case of OOK, although DPSK generally has a 3 dB higher SNR (signal-to-noise ratio) than OOK.