Abstract: In synthetic aperture radar imaging and application，the frequency rate needs to be estimated.The usual algorithm based on image contrast optimization needs iteration，so the computation of the algorithm is big，the constringency of the algorithm is tardy and the algorithm is inefficient.For conquering the defect，a new autofocus algorithm based on image contrast optimization is showed in this paper.The algorithm is named parabola method.The algorithm estimates Doppler rate by using parabola in mathematics.Without iteration， the efficiency of the algorithm is greatly improved.The airborne synthetic aperture radar(SAR) real data image result and analysis validate the feasibility and efficiency of given method in this paper.