Low reflectivity of microwave absorbers is important to improve the performance of anechoic chamber measurements. The shape of the absorber as well as the material used are among the main components to provide desired low reflection performance. Pyramidal and wedge-shaped absorbers are two of the most wellknown microwave absorber types. We discuss the effect of a convex shape on reflection performance of microwave absorbers and show that convex shape structure has significantly performance by absorbing most of the electromagnetic energy of the incident wave. We used a concavity theorem based design method to obtain a function for a convex shape. Absorbing structures have been analyzed by using the periodic moment method (PMM). An optimization method is employed to find coefficients of the convex function, which provides better absorption performance than the wedge type absorber. Reflection performances of the wedge and convex absorbers for the 2-12 GHz frequency band are compared. Their reflection performances at 2 GHz for different angles of incidence are presented. An important implication of this study is that the alternative absorber shapes other than the wedge shape are demonstrated by using simple mathematical methods to have the optimal reflection characteristics.