In order to improve the degree of freedom of the traditional parallel array, an improved two parallel co-prime array is proposed, an joint estimation method which combines sparse representation and least square method is utilized to estimate two-dimensional direction of arrival (DOA). Firstly, the cross-covariance matrix of the parallel co-prime array is constructed. Then, a virtual array with a large aperture is generated by vectorization, rearrangement and de-redundancy. Next, transform the two-dimensional DOA estimation problem to a one-dimensional DOA estimation problem. Furthermore, a sparse reconstruction problem of complex signals is formulated to estimate the azimuth, which is solved by second-order cone programming. Finally, the least square method is used to solve the elevation angle. This method can accurately estimate the azimuth and elevation of targets without the prior information of the target, and can achieve automatic pairing. Compared with the traditional parallel uniform linear array and the parallel co-prime array, the proposed array structure extends the virtual aperture of the array, improves the estimation accuracy and identifies more target sources. Simulation results demonstrate the effectiveness of the proposed method.