Detecting time-varying target in non-stationary background is difficult and attractive problem. Time-varying movement exists widely in radar and communication systems. The non-linear processing with higher moments is discussed in the situation. Firstly the signal model of time-varying target with fix acceleration is analyzed. Then the radar echoes from synthetic aperture radar (SAR) are processed with higher moments. It not only restrains Gaussian noise automatically, but also suppresses non-stationary noise. Time-varying targets are different from the non-stationary background clutters. Moreover, the influences of the shadows about time-varying targets are reduced in the algorithm of higher moments. The proposal mentioned above utilizes higher moments to avoid analyzing the complex electromagnetic wave propagation and scatter theory. The differences of detection probability are compared between the chip with time-varying target and the clutter chip. The performances among different number order moments are compared by processing lots of actual SAR data added non-stationary noise. Lastly, the suitable number order moments are suggested by comparing the results from processing the actual radar echoes.