Fourier ptychography (FP) is an effective approach capable of imaging with both large field-of-view (FOV) and high resolution, the published works have proven that the resolution is limited by the sum of the illumination numerical aperture (NA) and the NA of the objective lens used. A spatial- and spectral-constrained FP (spFP) reconstruction algorithm was introduced to improve the spatial resolution. Unlike the typical unconstrained algorithm, the proposed algorithm incorporated both spatial- and spectral-constraints based on the additional prior information extracted from the typical FP reconstruction, and it did not need any additional hardware or captured images. The proposed approach was based on an assumption that the image was known to be sparse. Both simulation and experimental results show that the spFP reconstruction improves the spatial resolution by ～26%, and also improves the contrast and general quality of the reconstructed image.