This letter proposes a new type of two-layer matching topology arranged on the inner surface of the car's bumper as the solution to suppress reflections of radar radio waves over a wide frequency range and incidence angles. To analyze the bumper system and to obtain the material properties of the matching layers, the Chebyshev multisection impedance matching transformer theory is adapted. The reflection coefficient at various automotive radar frequency bands is provided, showing a significant reduction in the reflections from the bumper that utilizes Chebyshev matching layers (CMLs). To demonstrate the efficacy of the proposed topology, CMLs are fabricated using 3-D printing technology and experimentally validated. Experimental results show that by utilizing CMLs, the transmission coefficient is improved by more than 1 dB, and the overall SNR improvement over the angular range of $0^{\circ }$ to $65^{\circ }$ varies between 2.21–8.69 dB, indicating an enhancement in the radar sensing range by 13.56%–64.9%. Also, the relative E-field map shows improvement in radar performance in both azimuth and elevation planes. Further, the E-field analysis of a finite conformal bumper shows that the losses due to the bumper with CMLs are approximately 1 dB less compared to the bumper.