In this paper, an aperture expanding direction finding algorithm using L-shaped non-uniform sparse array is proposed. Firstly, the virtual array is expanded by vectorization, de-redundancy and sorting of received data covariance matrix. Secondly, the full rank matrix is got by smoothing the virtual array data, and the signal subspace is obtained by matrix block processing and matrix operation. Finally, the elevation angle and azimuth angle are acquired by using the rotation invariant relation. The algorithm does not need to decompose the covariance matrix of the data, nor does it need to search the two-dimensional spectral peaks. It can greatly reduce the computational complexity when there are many array elements and large number of snapshots. The simulation results show that the sparse array arrangement can enlarge the array aperture, improve the parameter resolution and the accuracy of DOA estimation, and verify the effectiveness of the proposed algorithm.