Automotive millimeter-wave (MMW) synthetic aperture radar (SAR) systems can achieve high-resolution images of detection areas, providing environmental perceptions that facilitate intelligent driving. However, curved path is inevitable in complex urban road environments. Non-uniform spatial sampling, brought about by curved path, leads to cross-coupling and spatial variation deteriorates greatly, significantly impacting the imaging results. To deal with these issues, we developed an Extended Omega-K Algorithm (EOKA) for an automotive SAR with a curved path. First, an equivalent range model was constructed based on the relationship between the range history and Doppler frequency. Then, using azimuth time mapping, the echo data was reconstructed with a form similar to that of a uniform linear case. As a result, an analytical two-dimensional (2D) spectrum was easily derived without using of the method of series reversion (MSR) that could be exploited for EOKA. The results from the parking lot, open road, and obstacle experimental scenes demonstrate the performance and feasibility of an MMW SAR for environmental perception.