In order to reduce the mutual coupling between sensors, a kind of co-prime nested array with adjustable element spacing is proposed. The proposed array consists of two nested arrays with different element spacing and the smallest intervals of two sub-arrays are determined by two co-prime positive integers. As long as the positive integers are big enough, the smallest intervals of each sub-array can be far more than half the wave length of incident signal, hence the reduction of the mutual coupling effect between sensors to a negligible level. To eliminate the direction ambiguity caused by large element spacing, a direction of arrival (DOA) estimation algorithm based on fourth-order cumulants is proposed to get unambiguous direction estimation. Compared with some classical self-correcting methods, the proposed algorithm has a higher angle resolution and estimation precision. Simulation results have proved the improved performance of proposed algorithm.