This paper proposes a novel method for two-dimensional (2-D) direction-of-arrival (DOA) estimation of multiple signals employing a sparse L-shaped array structured by a sparse linear array (SLA), a sparse uniform linear array (SULA) and an auxiliary sensor. In this method, the elevation angles are estimated by using the SLA and an efficient search approach, while the azimuth angle estimation is performed in two stages. In the first stage, the rough azimuth angle estimates are obtained by utilizing a noise-free cross-covariance matrix (CCM), the estimated elevation angles and data from three sensors including the auxiliary sensor. In the second stage, the fine azimuth angle estimates can be achieved by using the shift-invariance property of the SULA and the rough azimuth angle estimates. Without extra pair-matching process, the proposed method can achieve automatic pairing of the 2-D DOA estimates. Simulation results show that our approach outperforms the compared methods, especially in the cases of low SNR, snapshot deficiency and multiple sources.