The continuous fractional Fourier transform (FRFT) can be interpreted as a rotation of a signal in the time-frequency plane and is a powerful tool for analyzing and processing nonstationary signals. Because of the importance of the FRFT, the discrete fractional Fourier transform (DFRFT) has recently become an important issue. We present the computation method for the DFRFT using the adaptive least-mean-square algorithm. First, the DFRFT computation scheme with single angle parameter of the signal block using the adaptive filter system is introduced. Second, considering the transform angles always change in practical applications, the DFRFT computation scheme with adjustable-angle parameter of the signal block using the adaptive filter system is presented. Then we construct two realization structures of the DFRFT computation with simultaneous multiple-angle parameters for each signal block. The proposed computation approaches have the inherent parallel structures, which make them suitable for efficient very large scale integration implementations.