We present a new algorithm for processing hybrid strip-map/spotlight SAR data which is based on a two-step focusing strategy. The first step performs an azimuth raw data filtering operation implemented via the (azimuth) convolution between the SAR data and a chirp signal with a properly chosen constant chirp rate. Following this step, the spectral folding of the azimuth raw signal spectrum is resolved and the space-variant characteristics of the system transfer function are preserved. Therefore, we can achieve the full focusing of the data by a conventional strip-map processing step implemented in frequency domain and requiring only a minor modification. The proposed algorithm is simple, efficient and has the unique feature of being suitable for processing strip-map, spotlight and hybrid strip-map/spotlight mode, the first two being particular cases of the more general last one. The presented experiments are carried out on simulated data relative to the COSMO/SkyMed sensors operating in the hybrid strip-map/spotlight mode; these results clarify the rationale of the proposed approach and confirm its validity.