With the aid of Fourier ptychographic microscopy, we can synthesize single-frame images with more details after spectrum expansion, thus reconstructing high-resolution images in a large field of view. However, the ubiquitous aberrations in imaging systems often lead to blurry images and reduce resolution of the reconstructed images. To solve the above problems, we proposed an innovative aberration correction method based on ptychographical iterative engine. Specifically, when updating the spectrum and pupil function, we adaptively selected the optimal ratio between their current and maximum values to improve the quality of iterative reconstruction. Then, we reconstructed the simulated images with mixed aberrations by taking peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as evaluation metrics. The simulation results showed that compared with the traditional embedded pupil recovery algorithm, our method sharply increased the PSNR and SSIM (14.9% and 1.4%, respectively). To further verify the effectiveness of our method on real images, we collected human blood cell samples for reconstruction. The reconstructed images were clear, which contributed to distinguishing the cell contours accurately.