Broadband sound absorption performance and high mechanical strength are major concerns for designing a microperforated plate (MPP) absorber, which is generally difficult to achieve for a single-layer MPP with straight holes. A MPP was proposed with variable cross-sectional holes, including large dents on one side, grooves on the other side, and intermediate micro-slits. The beneficial effects of the special geometrical features are thoroughly discussed and experimentally validated. Models to calculate the acoustic impedance are established, and acoustic behaviors within holes are simulated. It was found that the micro-slits could provide necessary acoustic resistance for impedance matching and very low reactance to expand sound absorption bandwidth. The large dents or grooves could provide the necessary thickness with negligible acoustic impedance to enhance plate mechanical strength. This research helps to implement a single-layer MPP design with good acoustical and mechanical performance.