In this letter, we propose a novel algorithm for sparse L-shaped array that addresses gain/phase uncertainties and off-grid direction of arrival estimation using compressed sensing theory. Firstly, the receiving signal of the sparse array is structured into an Errors in Variables model. Then, a novel algorithm termed IOMP-TLS is proposed for off-grid signal reconstruction and gain/phase uncertainties estimation based on an enhanced greedy algorithm. Finally, the simulations show that our proposed algorithm is superior to many other methods in estimation performance.