We consider the problem of direction of arrival (DOA) estimation using a newly proposed structure of co-prime arrays. A continuous sparse recovery method is implemented in order to increase resolution. We show that in the noiseless case one can theoretically detect up to MN/2 sources with only 2M+N sensors via continuous sparse recovery. The noise statistics of co-prime arrays are also analyzed to demonstrate the robustness of the proposed optimization scheme. Using numerical examples, we show the superiority of the proposed method.