Inspired by the key role of the coordination environment in the catalytic activity of enzymes, a rational design of the coordination structure of active sites at the atom scale is expected to develop high-performance enzyme-like catalysts. Here, we design a simple model system involving pentacoordinated and tetracoordinated Fe-N-C single-atom catalysts (named NG-Heme and G-Heme, respectively) to investigate structure-activity relationships. NG-Heme with axial ligand-engineered Fe sites exhibits superior enzyme-like activity to G-Heme, achieving the goal of vivid mimicking of the active sites of peroxidase. Experiments and theoretical studies reveal that the enhanced intrinsic catalytic activity originates from the "push effect" of the additional axial ligand, which can strengthen the interaction between the active site and the intermediate. Based on the outstanding catalytic activity, an NG-Heme-linked immunosorbent assay was constructed for colorimetric detection of carcinoembryonic antigen, exhibiting satisfactory sensitivity and feasibility in the analysis of clinical samples.