For synthetic aperture radar (SAR), a system impulse response with low sidelobes is very important because sidelobes may interfere with the nearby scatterers and contribute to multiplicative noise. It is well known that a nonlinear frequency-modulation (NLFM) chirp waveform can shape the signal's power spectral density and provide a radar matched filter output with lower sidelobes without loss of the signal-to-noise ratio when compared with the linear frequency-modulation chirp. These advantages make the NLFM waveform to be a promising candidate to improve the imaging quality for SAR. However, so far, to our knowledge, there is no real application of NLFM waveforms for SAR. This letter, for the first time, demonstrates the airborne SAR experiment using an NLFM waveform. In the underlying experiment, the construction of the NLFM signal is investigated and a modified range migration algorithm (RMA) is developed to adapt it for focusing the NLFM SAR data. Both simulation and experimental results exhibit the promising power of the NLFM chirp and show the accuracy of the proposed modified RMA.