Abstract: For the fast computation problem of MUSIC spectrum, a fast algorithm using effective phase modes in mode space of arbitrary array is proposed. During the computation process of spatial spectrum in different directions, phase shift factor of each element can form a series of new direction vectors. With certain transformation, the multiplication operation between the new direction vectors and eigenvectors in noise subspace has the characteristics of cyclic convolution, MUSIC spectrum can be realized by discrete Fourier transform (DFT). The new direction vectors are equivalent to sampling results of virtual continuous cycle array. According to the fact that the number of the effective phase modes excited by circular array is far fewer than MUSIC spectrum point, the computational complexity can be obviously decreased by using effective phase modes in the process of MUSIC spectrum computation through DFT. For the oversampling characteristics of direction vectors, effective phase modes can be obtained by the sequences after extraction of direction vectors, which can further reduce computational complexity. The simulation result verifies that the proposed algorithm is valid.