Synthetic Aperture Radar (SAR) is a high-resolution radar that operates all day and in all weather conditions, so it has been widely used in various fields of science and technology. Ship detection using SAR images has become important research in marine applications. However, in complex scenes, ships are easily submerged in sea clutter, which cause missed detection. Due to this, strong sidelobes in SAR images generate false targets and reduce the detection accuracy. To solve these problems, a ship detection method based on eigensubspace projection (ESSP) in SAR images is proposed. First, the image is reconstructed into a new observation matrix along the azimuth direction, and the phase space matrix of the reconstructed image is constructed by using the Hankel characteristic, which preliminarily determines the approximate position of the ship. Then, the autocorrelation matrix of the reconstructed image is decomposed by eigenvalue decomposition (EVD). According to the size of the eigenvalues, the corresponding eigenvectors are divided into two parts, which constitute the basis of the ship subspace and the clutter subspace. Finally, the original image is projected into the ship subspace, and the ship data in the ship subspace are rearranged to obtain the precise position of the ship with significantly suppressed clutter. To verify the effectiveness of the proposed method, the ESSP method is compared with other detection methods on four images at different sea conditions. The results show that the detection accuracy of the ESSP method reaches 89.87% in complex scenes. Compared with other methods, the proposed method can extract ship targets from sea clutter more accurately and reduce the number of false alarms, which has obvious advantages in terms of detection accuracy and timeliness.