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Three-dimensional (3-D) localization information, including elevation angle, azimuth angle, and range, is important for locating a single source with spherical wave-fronts. Aiming to reduce the high computational complexity of the classical 3-D multiple signal classification (3D-MUSIC) localization method, a novel low-complexity reduced-dimension MUSIC (RD-MUSIC) algorithm based on the sparse symmetric cross array (SSCA) is proposed in this article. The RD-MUSIC converts the 3-D exhaustive search into three one-dimensional (1-D) searches, where two of them are obtained by a two-stage reduced-dimension method to find the angles, and the remaining one is utilized to obtain the range. In addition, a detailed complexity analysis is provided. Simulation results demonstrate that the performance of the proposed algorithm is extremely close to that of the existing rank-reduced MUSIC (RARE-MUSIC) and 3D-MUSIC algorithms, whereas the complexity of the proposed method is significantly lower than that of the others, which is a big advantage in practice.