Magnetorheological energy absorbers (MREAs) have manifested their superiority as a controllable damper. An ideal feature for MREA is to remain a constant damping force within a certain impact displacement (referred to as plateau behavior) in the transient impact process. Realizing this plateau behavior by introducing the structure of drain hole is able to effectively reduce harmfulness from the overshoot to the buffered object. In this study, a radial flow mode MREA with a center drain hole configuration is proposed, in order to achieve an approximate plateau as well as to expand the dynamic range. The Power-Law model is employed to analyze the impact behaviors of the MREA due to its smooth shear stress-shear rate curve and simple mathematical form. Five parameters (i.e., plateau angle, radial flow velocity ratio, minor losses ratio, dynamic range ratio, and peak force ratio) are defined to characterize the effects of the drain hole quantitatively and comprehensively. The diameter of center drain hole is specially focused on because of its significant influences on the parameters. Two types of MREAs with/without drain holes are fabricated and tested using a drop tower facility with a 600 kg mass. The experimental results show that the plateau angle of MREA with drain hole is reduced by 56.1% compared to that without hole, and also demonstrate that the Power-Law based model is capable of well predicting the dynamic behavior of the MREA.