To investigate the influence of atmospheric turbulence on the image ofsynthetic aperture ladar (SAL),numerical simulation of phase screens following the Kolmogorov spectrum by using spectrum inverse transform is introduced and detailed pictures of monolayer or multilayer random phase screens are given,then the calculated multilayer random phase screens are used to simulate the real atmospheric turbulence. In an ideal monostatic airborne spotlight SAL imaging system,detailed calculations on the SAL images with point or extended targets through no,weak,medium and strong turbulence are illustrated. The results vividly show that the atmospheric turbulence can severely affecte the azimuth resolution of the SAL image and with the increase of the atmospheric turbulence,the distortion of the SAL image deteriorates. To correct the degraded SAL images induced by atmospheric turbulence,phase gradient algorithm (PGA) method is implemented in azimuth,and the effort shows a significant improvement in the guality of the SAL image.