An improved algorithm is presented for a signal's direction of arrival estimation to reduce the computational complexity of the existing modified multiple signal classification (MMUSIC) algorithm. In this paper, FFT algorithm is introduced to narrow the searching range of the direction angle. Afterwards, a compromise approach-based SVD and orthogonal-triangular decomposition takes the place of traditional double SVDs. Then, during matrix calculation, the noise subspace is achieved for the signal's direction of arrival. Finally, the system simulation demonstrates the efficiency and reliability of this novel MMUSIC algorithm. Compared with the existing algorithm, MMUSIC effectively saves the computational complexity with the approximation estimation performance.