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Density Tapered Arrays (DTA) with nonperiodic spaced elements have many interesting features when compared to traditional DTA in which antenna elements are located only at the intersections of periodic grid; however, a design method is yet to be fully develoed. A new approach is presented using Centroidal Voronoi Tessellations (CVT) to design DTA with nonperiodic element distributions proportional to the desired amplitude taper and with nonperiodic and ‘uniform’ properties. A 32.8λ diameter circular aperture array with 1656 elements is discussed and theoretical patterns are computed for density tapers modeled after −25 dB,−30 dB,−35 dB, and −40 dB circular Taylor distributions. The obtained sidelobe levels and aperture efficiency are better than heretofore reported.