In this letter, a novel long-time coherent integration method, known as the Radon-linear canonical transform (RLCT), is proposed for detection of a low observable moving target in sea clutter. The micro-Doppler (m-D) of a sea-surface target is studied and modeled as multiple linear-frequency-modulated signals, which result from the accelerated and 3-D rotated movements. The RLCT-based algorithm employs m-D as a useful signature for target detection and can simultaneously compensate the range and Doppler migrations during long observation time, which simplifies the operational procedure. By searching along the moving trajectory and using extra three degrees of freedom, the observation values of m-D signals can be well matched and accumulated as peaks in the RLCT domain. Then, the target can be declared by comparing the peak value with an adaptive threshold. The definition of the RLCT demonstrates that it is the generalization of the popular moving target detection, Radon-Fourier transform, fractional Fourier transform, and linear canonical transform methods. Finally, experiments using a real sea clutter data set show that the proposed method can achieve high integration gain and detection probability of a micromotion target in heavy sea clutter.