Moving target detection is of vital importance to maritime security and maritime resource protection. However, the detection of slow or weak targets is difficult based on traditional methods. A new detection method is proposed by using the different motion variations of radar moving target and sea clutter in the range-Doppler spectrum sequence. The first step in implementing this method is the separation of moving target and sea clutter by the low-rank representation, in which the target and clutter are modeled as foreground and background components. Subsequently, a sea clutter discriminator is constructed within the sea clutter bandwidth to further remove the sea clutter (false alarms) that exists in the foreground. The proposed method can reduce the sea clutter power while maintaining the target power and improve the detection rate of moving targets, especially slow or weak targets. Data collected with airborne maritime surveillance radar in maritime moving target indication (MMTI) mode are used to validate the performance of the proposed method. The experimental results demonstrate that the improvement in the signal-to-clutter ratio (SCR) obtained with the proposed method is better than that obtained with space-time adaptive processing (STAP, including 1DT-STAP, 3DT-STAP and sparse-STAP) and principal component pursuit (PCP) methods; additionally, the figure of merit (FOM) of the proposed method is higher than that of the constant false alarm rate (CFAR) and PCP method. Furthermore, the tracks of ships are obtained by applying a location constraint to the foreground sequence.