A Reduced-dimensional spherical harmonics MUSIC（RD-SHMUSIC） is proposed to solve the problem of high computational complexity of Multiple signal classification（MUSIC） algorithm for Twodimensional（2-D） Direction of arrival（DOA） estimation.The proposed algorithm first expresses the spherical harmonic steering vector as a linear weight of a uniform phase vectors. Via the Lagrange multiplier method, we can get a new search function to estimate elevations. At second step, the algorithm expresses the steering vector in another form, a linear weight of a vector which is constructed by associated Legendre functions. A search function to estimate azimuths can also be obtained.The proposed method only needs One dimensional（1-D） angle search, which means it has a large reduction of computational complexity compared to the traditional Spherical harmonics MUSIC（SHMUSIC）. The simulation results show that the accuracy of the proposed method is better than Two-stage decoupled approach（TSDA）algorithm, and has close performance to that of SHMUSIC.
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