High quality, highly efficient finishing processes are required for finishing difficult-to-machine materials. Magnetic abrasive finishing (MAF) process is a finishing method that can obtain a high accuracy surface using fine magnetic particles and abrasive particles, but has poor finishing efficiency. On the contrary, fixed abrasive polishing (FAP) is a polishing process can obtain high material removal efficiency but often cannot provide a high-quality surface at the nano-scale. Therefore, this work proposes a new finishing process, which combines the magnetic abrasive finishing process and the fixed abrasive polishing process (MAF-FAP). To verify the proposed methodology, a finishing device was developed and finishing experiments on alumina ceramic plates were performed. Furthermore, the mechanism of the MAF-FAP process was investigated. In addition, the influence of process parameters on finishing characteristics is discussed. According to the experimental results, this process can achieve high-efficiency finishing of brittle hard materials (alumina ceramics) and can obtain nano-scale surfaces. The surface roughness of the alumina ceramic plate is improved from 202.11 nm Ra to 3.67 nm Ra within 30 min.