Aiming at the problem that the traditional signal acquisition circuit needs a larger storage space to store data in the observation of radio astronomical signal, a hardware circuit design method for low frequency radio astronomical signal acquisition based on Modulated Wideband Converter (MWC) was proposed. Firstly, the observed signal was multiplied by four pseudo-random period signals, and then the results were divided into four channels. Secondly, the four-channel signals were filtered by second-order Butterworth low-pass filter repectively. Then, the four-channel filtered signals were sampled and the data were transferred to a Field-Programmable Gate Array (FPGA) for storage. Finally, the signal was reconstructed by Orthogonal Matching Pursuit (OMP) algorithm. The theoretical analysis and experimental results show that the Mean Square Error (MSE) between the reconstructed signal and the observed signal is 1.27×10 ^-2, and the compression rate of data storage space is 20%. The proposed hardware circuit design method reduces circuit design costs as well as storage space.