The constant false alarm rate (CFAR) detector is a classical algorithm for ship detection with synthetic aperture radar (SAR). However, the algorithm is susceptible to the accuracy of sea clutter modeling and the desired probability of false alarm, thus reducing detection performance. Therefore, a goodness-of-fit test and a certain number of ship detection experiments and theoretical analysis of false alarms have been extensively practiced as prior knowledge. Compared to earlier SAR sensors, the newly launched Sentinel-1 has nearly uniform signal-to-noise ratio, and the distributed-target-ambiguity ratio may provide additional capabilities for ship detection. Owing to the complex interaction between SAR system and sea surface, the previous work may not be completely suitable for Sentinel-1. As its application is in the beginning, further research is needed. We evaluate the effectiveness of model fitting among five commonly used distributions, and the influences of incident angle, polarization, and sea state on modeling are analyzed. In addition, CFAR detectors constructed by these distributions carried out the ship detection experiments. Moreover, the false alarms that are inevitably caused during the ship detection are classified and statistically analyzed. These aforementioned works can provide an important reference for Sentinel-1 to implement large-scale, as well as long-term, ship detection activities and for further improvement.