In order to distinguish true ship wakes from other spurious linear feature effectively, a novel method of ship wakes detection based on the Radon transform (RT) and on the entropy, and named joint Radon and entropy detection algorithm (JRE) is proposed. The proposed approach extracts all possible peaks in Radon transform space with a low threshold, then computes the entropies centering around each peak and identifies the true ship wakes from spurious ones. Furthermore, the method can increase the detection probability and reduce the false alarm probability. Theoretical analysis and experimental results show that the method is capable of detecting synthetic aperture radar (SAR) ship wakes precisely and reliably in the presence of both strong noise and sea clutter