This paper proposes an autofocus algorithm used for Synthetic Aperture Radar (SAR) images, called Adaptive Kurtosis Optimization Autofocus Algorithm (AKOAA). The AKOAA can reduce the differ-ence between initial value and real value in focusing by adaptively adjusting the initial value, therefore effec-tively improve the local extremum problem in the Contrast Optimization Autofocus Algorithm (COAA) and speed up the convergence velocity. The principle and realization method of AKOAA are thoroughly investi-gated, and experimental results using real L-band SAR data show that the focus speed of AKOAA is nearly doubled compared with that of the COAA, and the image contrast of AKOAA is improved as well. This paper proposes an autofocus algorithm used for Synthetic Aperture Radar (SAR) images, called Adaptive Kurtosis Optimization Autofocus Algorithm (AKOAA). The AKOAA can reduce the differnce between initial value and real value in focusing by adaptively adjusting the initial value, therefore effec-tively improve the local extremum problem in the Contrast Optimization Autofocus Algorithm (COAA) and speed up the convergence velocity. The principle and realization method of AKOAA are thoroughly investi-gated, and experimental results using real L-band SAR data show that the focus speed of AKOAA is nearly doubled compared with that of the COAA, and the image contrast of AKOAA is improved as well.