The Imaging Science Subsystem (ISS) mounted on the Cassini spacecraft has taken a lot of images, which provides an important source of high-precision astrometry of some planets and satellites. However, some of these images are degraded by trailed stars. Previously, these degraded images cannot be used for astrometry. In this paper, a new method is proposed to detect and compute the centers of these trailed stars automatically. The method is then performed on the astrometry of ISS images with trailed stars. Finally, we provided 658 astrometric positions between 2004 and 2017 of several satellites that include Enceladus, Dione, Tethys, Mimas and Rhea. Compared with the JPL ephemeris SAT427, the mean residuals of these measurements are 0.11 km and 0.26 km in R.A. and decl., respectively. Their standard deviations are 1.08 km and 1.37 km, respectively. The results show that the proposed method performs astrometric measurements of Cassini ISS images with trailed stars effectively.