The covariance matching criterion (CMC) has been successfully utilized in one-dimensional DOA estimation, resulting in some representative gridless methods. In this paper, we extend this criterion into two-dimensional (2-D) DOA estimation in the case of L-shaped arrays. In particular, we utilize the cross-covariance matrix of the array output to formulate a single measurement vector (SMV) model and then propose a semidefinite programming by minimizing the CMC with respect to the SMV model. Finally, the DOAs are estimated by applying 2-D ESPRIT to the estimated covariance of the SMV output. Our proposed method can be applied to both uniform and sparse L-shaped arrays. We also show that the computational complexity of our method is proportional to the number of sensors rather than the aperture of the array, and hence the computational cost can be reduced if we properly eliminate some sensors. Simulation results are provided to demonstrate the advantage of our method.