A microwave photonic compressive sensing radar is proposed for distance measurement based on cascaded Mach-Zehnder modulators (MZMs). In the transmitter, a dual-parallel Mach-Zehnder modulator (DPMZM) is used to generate the quadrupled linearly frequency-modulated (LFM) signals. In the receiver, the echo signal can be de-chirped and the de-chirped signal can be mixed with a pseudo-random bit sequence (PRBS) in the optical field by using cascaded MZMs. Then the mixed signal can be acquired by a low pass filter (LPF) and sampled at a sub-Nyquist sampling rate by using a low-speed analog-to-digital converter (ADC). Finally, orthogonal matching pursuit (OMP) algorithm can be used to recover the de-chirped signal. The results of the simulation and proof-of-concept experiment demonstrate that when the data compression ratio is 8, the system can reconstruct the frequency of the de-chirp signal with less observed value and the distance measurement error is less than 2cm. In addition, it reduces the pressure of data sampling, storage and information processing, and it breaks Nyquist sampling theory.