In this Letter, we present a learning-based method for efficient Fourier single-pixel imaging (FSI). Based on the auto-encoder, the proposed adaptive under-sampling technique (AuSamNet) manages to optimize a sampling mask and a deep neural network at the same time to achieve both under-sampling of the object image's Fourier spectrum and high-quality reconstruction from the under-sampled measurements. It is thus helpful in determining the best encoding and decoding scheme for FSI. Simulation and experiments demonstrate that AuSamNet can reconstruct high-quality natural color images even when the sampling ratio is as low as 7.5%. The proposed adaptive under-sampling strategy can be used for other computational imaging modalities, such as tomography and ptychography. We have released our source code.