Fourier single-pixel imaging (FSI) has been proven to achieve excellent image quality when sampling all information in the Fourier domain. However, when the size of an imaging target is large, fully sampling Fourier coefficients would result in a large waste of sampling resources. An adaptive sampling method is proposed that is simple to implement and effectively improves the reconstructed image quality from undersampled Fourier coefficients. Through a rough estimation of spectrum energy distribution, the adaptive sampling trajectory is generated by the designed adaptive probability density function. Both the results of computational simulations and experiments demonstrate that the proposed method has overcome the limitations of the insufficient sampling rates, and the reconstruction images have obtained dramatic improvements. These improvements greatly promote the development of the FSI during undersampled conditions.