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This paper addresses the problem of direction of arrival (DOA) estimation by exploiting the sparsity enforced recovery technique for co-prime arrays, which can increase the degrees of freedom. To apply the sparsity based technique, the discretization of the potential DOA range is required and every target must fall on the predefined grid. Off-grid target can highly deteriorate the recovery performance. To the end, this paper takes the off-grid DOAs into account and reformulates the sparse recovery problem with unknown grid offset vector. By introducing a convex function majorizing the given objective function, an iterative approach is developed to gradually amend the offset vector to achieve final DOA estimation. Numerical simulations are provided to verify the effectiveness of the proposed method in terms of detection ability, resolution ability and root mean squared estimation error, as compared to the other state-of-the-art methods. [ABSTRACT FROM AUTHOR]