On-grid approaches for DOA estimation majorly exhibits the problem of grid mismatch. Coarse grid leads to reduced estimation accuracy and dense grid leads to increased algorithm complexity and performance degradation due to highly correlated array manifold matrix. In this paper, a fixed off-grid DOA estimation algorithm is proposed to overcome this grid mismatch problem. Firstly, a sparsity based linear interpolation model for array manifold matrix is proposed to avoid the above limitation by introducing a bias parameter into the estimation framework. To solve this model, an Auto-regression (1) (AR (1)) based sparse Bayesian learning algorithm is proposed. To exploit the temporal correlation property of unknown DOA spatial spectrum in a MMV case, we develop this AR (1) model along with SBL to estimate the unknown DOA spectrum and expectation maximization (EM) framework to update the hyper-parameters. The results section shows that the proposed algorithm enjoys good estimation resolution and accuracy in the cases of fewer snapshots available, highly correlated signal sources, very low SNR and very closely spaced sources.