In this work, the staggered SAR technique is employed for high-speed platform highly-squint SAR by varying the pulse repetition interval (PRI) as a linear function of range-walk. To focus the staggered SAR data more efficiently, a low-complexity modified Omega-k algorithm is proposed based on a novel method for optimal azimuth non-uniform interpolation, avoiding zero padding in range direction for recovering range cell migration (RCM) and saving in both data storage and computational load. An approximate model on continuous PRI variation with respect to sliding receive-window is employed in the proposed algorithm, leaving a residual phase error only due to the effect of a time-varying Doppler phase caused by staggered SAR. Then, azimuth non-uniform interpolation (ANI) at baseband is carried out to compensate the azimuth non-uniform sampling (ANS) effect resulting from continuous PRI variation, which is further followed by the modified Omega-k algorithm. The proposed algorithm has a significantly lower computational complexity, but with an equally effective imaging performance, as shown in our simulation results.