A novel method for reducing the impact of non-ideal pseudo-random binary sequence (PRBS) on microwave photonic random demodulators (RDs) in a photonics-assisted compressed sensing (CS) system is proposed. Different from the commonly used method that switches the bias point of the optical modulator in the RD between two quadrature transmission points to mix the signal to be sampled and the PRBS, this method employs a PRBS with lower amplitude to low bias the optical modulator so that the impact of non-ideal PRBS on microwave photonic RDs can be greatly reduced by compressing the amplitude of non-ideal parts of the PRBS. An experiment is performed to verify the concept. The optical modulator is properly low-biased via PRBS amplitude compression. The data rate and occupied bandwidth of the PRBS are 500 Mb/s and 1 GHz, while the multi-tone signals with a maximum frequency of 100 MHz are sampled at an equivalent sampling rate of only 50 MSa/s. The results show that the reconstruction error can be reduced by up to 85%. The proposed method can significantly reduce the requirements for PRBS in RD-based photonics-assisted CS systems, providing a feasible solution for reducing the complexity and cost of system implementation.