Benefiting from the development of compressed sensing (CS) theory, sparse representation based off-grid direction-of-arrival (DOA) estimation technique has been extensively exploited, resulting in several high accuracy methods. However, most of these methods are based on the grid assumption, i.e., the DOAs of the incident signals are accurately located on the grid points, which violates the fact that the true DOAs belong to the continuous angle space. This grid bias effect may bring in model mismatch, leading to performance deterioration. In this paper, we propose an off-grid signal model based on Taylor expansion, which allows the DOAs to deviate from the grid points, so the grid bias effect can be eliminated, and the estimation accuracy can be improved. We employ an alternating iterative method to solve the problem and use the singular value decomposition to reduce the computational cost. The proposed method is able to reduce the grid bias, resulting in high estimation accuracy. Simulation results are provided to verify the effectiveness of the proposed method.