A simple and all-optical Doppler frequency shift (DFS) measurement system is presented. It is based on a dual-drive Mach Zehnder modulator (DDMZM) driven by a transmitted signal and an echo signal received by an antenna. A low-frequency sawtooth wave is applied to the DDMZM DC port to frequency shift the carrier and sidebands generated by the transmitted signal. Beating of a frequency-shifted transmitted signal sideband and an echo signal sideband at the photodetector produces a low-frequency electrical signal. The DFS, and consequently the speed and moving direction of a target, can be obtained from the frequency of this low-frequency electrical signal. The DDMZM used in the proposed DFS measurement system does not need to be operated at a specific point in the transfer function and hence it has no bias drift problem. The proposed DFS measurement technique can be used in both CW and pulsed radar systems. Experimental results demonstrate the proposed DFS measurement system has a wide operating frequency range of 10 GHz to 19.95 GHz, small DFS measurement error of less than 0.6 Hz and long-term stable performance. Results also demonstrate, for the first time, DFS measurement of a pulsed signal using a microwave photonic technique.