We consider the problem of two-dimensional (2-D) angles of arrival estimation using a newly proposed structure of nonuniform linear array, referred to as nested coprime array with compressed inter-element spacing (CACIS). By constructing a cross-correlation matrix of the received signals, the nested CACIS exhibits a larger number of degrees of freedom. A two-step weighted l₁-norm penalty strategy is proposed to fully utilize these degrees of freedom, where the weight matrices are constructed by MUSIC spectrum function and the threshold function, respectively. The proposed method has several salient advantages over the compared method, including increased resolution and accuracy, estimating many more number of sources and suppressing spurious peaks efficiently. Simulation results validate the superiority of the proposed method.