Many Fourier ptychography microscopy techniques have been proposed to achieve higher recovery accuracy in the past few years, yet it is little known that their reconstructed quality is also dependent on the choice of recovery sequence, which is important for fast solution convergence during the Fourier ptychography reconstruction process. In this paper, we propose to use the Hilbert fractal curve, which is one of the most representative of classic space-filling curves, as a new kind of recovery sequence of mesh LED arrays and validate its effectiveness and robustness with both simulated and real experiments. Results show that the Hilbert fractal curve as the recovery sequence is a better choice for periodic LED arrays, compared with raster line, spiral line, and wave-shaped-curve three-recovery sequences.