When the off-grid signals appear, the grid mismatching will lead to the serious performance degradation in compressed sensing direction of arrival (DOA) estimation. To address this issue, an off-grid signal DOA estimation algorithm under compressed sensing framework is proposed based on the Khatri Rao transform of received data covariance matrix and the orthogonal decomposition of steering vector. A new steering vector model of off-grid signal is created according to the orthogonality between signal steering vector and its first derivative. The grid deviation is estimated based on the least square theory. To increase the accuracy of sparse reconstruction, the iterative least squares subspace estimation (ILLSE) is adopted to estimate noise covariance matrix in constructing the sparse reconstruction model. The simulation results show that the proposed algorithm has good performance on off-grid signal DOA estimation under different signal to noise ratios and grid spacings.