According to the sparsity of the channel response, a multipath time-delay estimation model based on compressed sensing(CS) was proposed in frequency domain, by which the time-delay estimation was converted into sparse vector estimation from undersampled data. Because partial DFT (Discrete Fourier Transform)matrix satisfied restricted isometry property(RIP) and the channel response was sparse, according to the CS theory, the required amount of data for the estimation was sharply decreased. The reason that the proposed method owned subchip multipath estimation ability and excellent anti-noise property was also analyzed. Then the time-delay estimation performance of CS method, MUSIC(Multiple Signal Classification) algorithm and ESPRIT(Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm were compared. The simulation and analysis showed that the proposed method owned super-resolution performance in subchip multipath time-delay estimation without prediction of the number of multipath and was superior to MUSIC and ESPRIT algorithms on certain conditions.