Moving target detection in Ultra-Wideband (UWB) SAR is associated with long integration time and has to handle azimuth focusing for reliable detection. This paper presents the theory and simulation results of the Fast Detection of Moving Targets by Focusing method (FDMTF) which is understood as the Detection of Moving Targets by Focusing method (DMTF) incorporating fast time-domain algorithms in the process. Two fast time-domain algorithms Fast Backprojection (PBP) and Fast Factorized Backprojection (FFBP) are considered. The results show that FDMTF performs very efficiently and still retains the ability of detection.