This paper investigates the delay-Doppler estimation problem of a pulse-Doppler radar which samples and quantizes the noisy echo signals to one-bit measurements.By applying a multichannel one-bit sampling scheme, we formulate the delay-Doppler estimation as a structured low-rank matrix recovery problem.Then the one-bit atomic norm soft-thresholding method is proposed to recover the low-rank matrix, in which a surrogate matrix is properly designed to evaluate the proximity of the recovered data to the sampled one.With the recovered low-rank matrix, the delays and Doppler frequencies can be determined and paired.Numerical experiments are performed to demonstrate the effectiveness of our method compared with the one-bit sparse signal recovery method based on discrete dictionary.