By iteratively stitching together the series of low-resolution (LR) images captured by either various small-aperture illuminations or angle-varied illuminations, the Fourier ptychography (FP) can recover large space-bandwidth- product (SBP) and high-resolution (HR) object images. The FP has been considered to be promising in various computational imaging fields. However, the illumination-based FP is limited by strict requirements of the objects which must be thin and satisfy the one-to-one mapping relationship in the Fourier plane, and the aperture-scanning Fourier ptychography is also limited by the long-time scanning and stable scanning mechanical structures requirements even though it can achieve super-resolution macroscopic imaging. Furthermore, the position and shape of the scanning aperture must be accurately modeled for the reconstruction, otherwise false object images may be output. Herein, based on the 4-f optical correlator structure, we proposed a novel method, termed variable-aperture Fourier ptychography, for reconstructing HR images from series of LR images. The numerical simulations illustrated that the variable-aperture Fourier ptychography can use a small number of LR images to reconstruct the object images, The experiments demonstrated that a high-quality object image with better resolution and contrast than other schemes, include direct imaging based on 4-f system and aperture scanning FP, can be obtained by our method. Two additional experiments proved that it is almost unaffected by the position and shape of the apertures.