Abstract: According to the fast computation problem of MUSIC spectrum in two dimensional direction of arrival estimation, the fast algorithms by manifold transformation or spectrum function transformation are studied. The implementation steps of computation method for two dimensional MUSIC spectrum by these algorithms are summarized. Furthermore, expressions for computational complexity of discussed algorithms in computing two dimensional MUSIC spectrum are presented. With reference to the conventional method, the ratio of computational complexity of discussed algorithms is compared. Meanwhile, for different circular arrays, the direction finding performance of applicable algorithms is compared by simulation. It is proved that the MUSIC algorithm based on Manifold Separation (MS-MUSIC) and Fast Fourier Transformation (FFT) which suits to arbitrary circular array (ACA-FFT-MUSIC) have higher engineering value according to the results of analysis and comparison. The performance and timeliness of direction finding system can be ensured by individual use of each method in whole frequency or combined use of the two in different frequency band based on different conditions.