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The mutual coupling among various components of the collocated crossdipole (CCD) vector-sensor is severe, and its application is greatly limited. The spatial spread dipole (SSD) vector-sensor can avoid this problem, but the multiple signal classification (MUSIC) algorithm for the SSD array is rarely developed. In view of this situation, this paper proposed a MUSIC-like algorithm for the SSD array. The biquaternion model was first established, and the biquaternion MUSIC (BQ-MUSIC) algorithm was developed on the basis of this model, for the two-dimensional direction-of-arrival (2D-DOA) estimation. Our proposed algorithm requires low computational complexity by adopting the dimensionality reduction method. Numerical simulations verify the effectiveness of the proposed algorithm.