In this paper, conventional Hilbert transform sampling method is generalized to fractional Hilbert transform sampling method. First, a frequency-domain analysis method is applied to derive the fractional Hilbert transform sampling theorem of a band-limited signal. Then, an analog filter bank method is presented to recover the original continuous-time signal from the discrete-time sampled signals. Because the analog filter bank is not easy to be implemented, a digital filter bank method is proposed to solve the reconstruction problem. Next, a sparse design of digital reconstruction filters is studied to reduce the arithmetic implementation complexity using sparse FIR filter design techniques. Finally, several numerical examples are illustrated to show the effectiveness of the proposed fractional Hilbert transform sampling method and its filter bank reconstruction.