Abstract: Curvilinear SAR (synthetic aperture radar) 2-D signal model and 3-D signal model were studied. The curvilinear SAR echo signal mathematic equation was derived. Iterative algorithm was applied to curvilinear SAR. According to minimum non-linear variance criteria, RELAX algorithm cost function in curvilinear SAR was founded. Every procedure in 2-D RELAX algorithm and 3-D RELAX algorithm was studied in detail. The target scatter amplitude and position can be estimated. The recursive idea was presented. The convergence condition was given. The characteristic and computation for RELAX algorithm were analyzed. RELAX algorithm can converge quickly and its computation is comparatively small. Rigorous convergence condition can increase RELAX algorithm computation. The analysis provides direction for curvilinear SAR data 3-D information extraction with iterative algorithm.