A new rank reduction (RARE)-based two-dimensional (2-D) direction of arrival (DOA) estimation algorithm is proposed considering a mixture of circular and strictly noncircular sources. To enhance array aperture, a geometry of three uniform linear arrays is considered and then treated as displaced arrays from a virtual array using a simple linear transformation. The received data and the conjugated counterpart are combined together, exploiting the noncircular property. Both sources can be estimated separately by designing and exploiting the distinctive nature of circular and noncircular steering vectors. However, a 2-D spectrum search would lead to a high computational complexity burden. To reduce this high computational complexity burden, a novel RARE-based method is proposed, which plays a vital role by decomposing 2-D observation space into two successive 1-D peak search functions. The proposed method has some distinctive advantages: it can enhance the array aperture utilization, it can provide better estimation accuracy when mixed sources are greater than the number of sensors, it can estimate a larger number of mixed sources than the number of sensors, and finally it can automatically pair 2-D DOAs without any complicated pairing formulation. Extensive simulation results are provided to demonstrate the effectiveness of the proposed method.