The original nonlinear chirp scaling (NCS) algorithm was extended for high precision processing of the highly squinted curvilinear trajectory synthetic aperture radar (CTSAR). Based on the analysis of slant range model and the frequency spectrum characteristics of the echo signal, a novel nonlinear chirp scaling function and more complex phase compensation factors with both velocity and acceleration parameters were proposed in the new algorithm for accommodation to curvilinear trajectory. The processing flow and computational complexity of modified NCS algorithm were fundamentally the same as the original NCS algorithm. However, the higher order phase compensation, range cell migration correction (RCMC) and range-variant secondary range compression (SRC) caused by the non-linear aperture and the severe range-azimuth coupling were accomplished accurately and efficiently without interpolation. Simulation results show that data acquired with a curvilinear aperture and a squint angle up to about 50° for X-band can be processed with no evident degradation of impulse response function.