Recently, Compressive Sensing (CS) has been applied to array signal processing. In theory, Direction-of-Arrival (DOA) estimation based on CS recovery can work well in correlated environments. However, a large number of sensors (i.e., linear measurements) are still needed for CS recovery. To improve on this, we propose a new CS-based DOA estimation method with a recently designed antenna structure called the Asymmetric Antenna without Phase Center (Asym-AWPC). The best reconstruction is achieved by solving the l1-norm optimization problem, which is cast as an l1-regularized least-squares program. Simulated results indicate the effectiveness of the proposed CS-based Asym-AWPC DOA estimator in a multipath environment over a recent Asym-AWPC DOA estimator but using the Multiple Signal Classification (MUSIC) rather than CS. Further improvement on the resolution can be achieved by tuning the degree of asymmetry in designing the Asym-AWPC.